well compact,

My mind as generous, and my shape as true

As honest madam's issue?  Why brand they us

With base?  With baseness?  Bastardy?  Base, base?

And he goes on to point out that "in the lusty stealth of nature" that he is fare more fit and suited to have position and power that the those that come from "a dull, stale, tired bed"  -- meaning his brother.  This argument is Edmund's reasoning for convincing his father to believe that his brother is a turncoat.  In this soliloquy, Edmund examines his own "nature" as contrasted with that of his more do-gooding brother and finds his own qualities of person, not birth, to render him the superior man.

Later, once Gloucester has swallowed Edmund's story, hook-line-and-sinker, Shakepseare brings in the other meaning of "nature" when Gloucester, searching for some external cause that his true and loyal son Edgar should turn against him, blames Nature, by way of cursing the aligment of the moon and stars.  He says:

These late eclipses in the sun and moon portend no good to us.  Though the wisdom of Nature can reason it thus and thus, yet Nature finds itself scourged by the sequent effects:  love cools, friendship falls off, brothers divide. . .in palaces, treason; and the bond cracked 'twixt son and father.

And Edmund ends this part of the scene with a scornful dismissal of this superstitious appraisal of Nature.  He does not believe that the events of the stars decide his future.  He believes himself to be the architect of his future not the external movements of the natural world.  So Edmund believes it to be his own "nature" rather than "Nature" that decides his course.

In this scene the meaning of nature (as being one's character and tendency towards certain behaviours) is contrasted with the forces of the natural world (ie Nature).  For more on "nature" in this play and Act I, scene ii, please follow the links below.

The two views of nature are of nature as good, and nature as evil. 

Edmund views nature in a good light.  Edmund opens in a soliloquy praising nature as a "Goddess" and seeking fortune for "Bastards" (illegitimate children) like himself.  He praises nature for convincing him to forge a letter from his brother Edgar, expressing a plot against the Earl of Gloucester. 

The Earl of Gloucester presents nature as being full of evils including the "late eclipses in the sun and moon" that have seemingly turned his legitimate son, Edgar, against him.

Nature and the natural world are important themes in Shakespeare's King Lear, and their importance is especially apparent in Act III, Scene 2. In this scene, Lear and his Fool wander out into the wilderness after being rejected by both of Lear's supposedly loving daughters, and Lear rages against the stormy weather, addressing Nature directly as if it were a living entity: 

Blow, winds, and crack your cheeks! rage! blow!
You cataracts and hurricanoes, spout
Till you have drenched our steeples, drowned the cocks!
You sulphurous and thought-executing fires,
Vaunt-couriers to oak-cleaving thunderbolts,
Singe my white head! And thou, all-shaking thunder,
Smite flat the thick rotundity o' the world! (1-7)

From Lear's address, we begin to see nature as a chaotic, disorderly force that lacks rhyme or reason. Indeed, in this scene it seems as if nature directly mirrors the chaos in Lear's own life. As such, the theme of nature in King Lear often presents the natural world as a chaotic, disorderly realm that undermines humanity's conception of an organized and rational universe. As such, through the theme of a chaotic nature, Shakespeare suggests traditional conceptions of meaning and order are not as steady as they once were, and human life is at the mercy of a natural world that has no qualms with squashing the lives of humans at random.

In the Elizabethan Age, the idea of world order is essential. This Chain of Being is essential to the structure of Shakespeare's dramas, the psychology of his personages, the "imagery that informs their speeches, and the fates they must confront." When this Chain of Being is disrupted, chaos occurs. In Act I Edmund speaks of his half-brother in a speech of much foreboding,

...his is the excellent foppery of the world,
that, when we are sick in fortune—often the surfeit
of our own behavior,—we make guilty of our disasters
the sun, the moon, and the stars: as if we were villains
by necessity; fools by heavenly compulsion; knaves,
thieves, and treachers, by spherical predominance; (1.2.114-119)

In Act III, this interconnection through the Chain of Being of disruption of the order of Lear's family and the "foul weather" is illustrated as ridicule of "the little world of man," but, at the same time, it reflects the human world, mirroring  the "division" in the kingdom. Thus, when Lear's kingdom becomes disturbed with the machinations of Edmund and the excesses of the other characters, who love or hate too much, so, too does the cosmos reflect this excess. Both Lear's and Edgar's loves are catastrophes, hence the storms of nature. For instance, in Act II, Lear rages against his two daughters,

I will have such revenges on you both

That all the world shall—I will do such things—

What they are yet I know not, but they shall be

The terrors of the earth. You think I’ll weep?

No, I’ll not weep. (2.4.276-280)

Storm and tempest [stage directions]

Nature plays a prominent role in William Shakespeare’s King Lear, both metaphorically and as a plot element propelling action.  The metaphorical use of nature is strongly implied throughout King Lear, a somewhat grim story in which an aging monarch’s own daughters plot against him.  It is against the backdrop of this palace intrigue that Shakespeare’s use of metaphors – in this case, comparing the growing sectarian conflict with the raging of the storm occurring both outside the castle walls and inside the king’s mind.  In the opening of Act III, Scene II, Lear is conversing with the Fool (or court jester), who enjoys the rare privilege of speaking candidly, if comically, to the highest authority in the land, a privilege accorded no other human being.  As Lear rages against the machinations of his daughters, his language is replete with references to raging storms:

“Blow, winds, and crack your cheeks! rage! blow!
You cataracts and hurricanoes, spout
Till you have drench'd our steeples, drown'd the cocks!
You sulphurous and thought-executing fires,
Vaunt-couriers to oak-cleaving thunderbolts,
Singe my white head! And thou, all-shaking thunder,
Smite flat the thick rotundity o' the world!
Crack nature's moulds, an germens spill at once,
That make ingrateful man!”

. . .

“Rumble thy bellyful! Spit, fire! spout, rain!
Nor rain, wind, thunder, fire, are my daughters:
I tax not you, you elements, with unkindness;
I never gave you kingdom, call'd you children,
You owe me no subscription: then let fall
Your horrible pleasure: here I stand, your slave,
A poor, infirm, weak, and despised old man: . . .”

This is a lengthy quote from Scene II, but it captures Shakespeare’s use of nature as a metaphor for the emotional turbulence within the kingdom.  These metaphorical references to the weather occur throughout the play, and gain in momentum in direct correlation to the story’s approaching climax, in which the king angrily departs the castle and wanders into a raging thunderstorm – a powerful metaphor for the raging storm from which he seeks to escape.

Lear is not alone in referencing nature as a metaphor for human emotions.  Favorite, but spurned daughter Cordelia similarly, in Scene IV, laments the chain of events that has transpired and seeks a proper resolution to the divisions within her family.  Addressing the court physician and soldiers, Cordelia states:

“Alack, 'tis he: why, he was met even now
As mad as the vex'd sea; singing aloud;
Crown'd with rank fumiter and furrow-weeds,
With bur-docks, hemlock, nettles, cuckoo-flowers,
Darnel, and all the idle weeds that grow
In our sustaining corn. A century send forth;
Search every acre in the high-grown field,
And bring him to our eye.”

Shakespeare’s use of nature in King Lear is as prominent as can possibly be.  Since the ancient Greeks and tales of the god Poseidon, weather has been used to convey emotions.  Storms are a perfect metaphor for human emotions run amok, and Shakespeare utilized them to the fullest extent.

In act 3, scene 2, King Lear finds himself upon a heath, essentially homeless. Two of his daughters, Goneril and Regan, have ordered that their doors be locked against their father.

While on the heath, a wild storm rages, echoing the inner turmoil that Lear is himself experiencing. Lear shouts at the storm,

Blow, winds, and crack your cheeks! Rage! Blow!
... spout
Till you have drench'd our steeples, drown'd the cocks!

In this quotation, Lear gives the audience a good idea as to just how violent the storm is, and at the same time, he reveals his own extreme anguish and distress. The violence of the storm serves here as a representation of what is happening inside of King Lear's mind. The desolate and exposed setting of the heath emphasizes his vulnerability and loneliness.

It is significant that the storm breaks just as King Lear leaves his daughters, Regan and Goneril, and just after he tells his fool,

I'll not weep ... this heart
Shall break into a hundred thousand flaws,
Or ere I'll weep. O fool, I shall go mad!

The stage direction immediately after King Lear says this indicates, "Storm and tempest." The fact that the storm breaks at this moment implies that although King Lear refuses to weep outwardly, he is weeping inwardly.

Shakespeare here uses the storm to show the audience how King Lear is feeling inside, as if to compensate for King Lear's refusal to show how he is feeling on the outside. At the same time, the breaking of the storm here indicates that this moment, when he is effectively cast out by his two daughters, Regan and Goneril, represents the beginning of his descent into madness.

And I would add one last comment:  Lear ends with the implication that nature lacks a reason, that perhaps the universe lacks rational meaning in spite of our attempts to infuse it with such. That, perhaps, is the significance of Cordelia's death:  the play could end satisfactorily without that, but no, she dies, apparently for no real reason.  Critic Frank Kermode calls this Shakespeare's cruelest play for that very reason--that Shakespeare posits a universe that lacks moral justification for events. For that reason, many critics find it is the most relevant of Shakespeare's play for the 20th and 21st centuries, in the aftermath of the holocaust, genocide, and constant war.

To expound on the previous post, for the noble characters in the play, namely Kent, Gloucester, the Fool, Cordelia, and Edgar, the ‘Reason’ of the ‘natural’ world order is to remain loyal to and preserve the orthodox view of ‘nature,’ (which maintains that the established social order should be respected and maintained) regardless of the suffering they must endure. There is a contrasting theory of ‘Reason’ of the ‘natural’ world orderi n the play however. For the evil characters, namely Regan, Goneril, Cornwall, Oswald, and Edmund, the ‘Reason’ is to destroy the ‘natural’ world order. These characters wish to topple the orthodox hierarchy, using whatever means necessary, and place themselves atop a new one.

Of course, the storm that rages during the play, with Lear himself caught in it, is a physical manifestation of nature itself raging against this upheavel.

I am not exactly sure what you mean by "related to nature," but what I would say is that this play uses nature as a metaphor.

The most obvious example of this comes in Act III, Scene 2.  In that scene, Lear is out on the heath in the storm.  He is being beaten up by the elements.  This is meant to symbolize the way in which the human world is treating him -- it is beating him up and is now beyond his control.

We get a glimpse of this as well when Lear disowns Cordelia in the first scene of the play.  He swears by various natural forces that she is not his daughter anymore.

So the powers of nature seem to be used as a metaphor for more human things -- for the forces that people use for their own purposes.