One of the most touching moments dealing with clothing in King Lear occurs near the very end of the play, just before Lear himself dies after having discovered the death of his daugher Cordelia. After Lear laments her death and addresses her dead body, he says to someone (Edgar? Kent?), "Pray you undo this button. Thank you, sir" (5.3.310).
Presumably he refers to a button on his own clothing, although it is also possible that he refers to some button on Cordelia's clothing. In the latter case, he might still be hoping, desperately, to offer her some physical comfort.
If it is Lear himself who needs such comfort, then this small detail makes him an even more pathetic and sympathetic figure. At one time, he was immensely powerful; now he is constrained by a simple button which he himself cannot undo. At one time, he was arrogant and unthankful; now he is courteously thankful even for such a small gesture as the undoing of a button.
It is partly through the inclusion of such seemingly "small" details that Shakespeare shows his supreme talent as a dramatist.
Shakespeare uses clothing in King Lear as a metaphor for Lear's struggles and epiphanies. Once he sheds his clothes, he sheds some of his inner arrogance and pride that recognizes (sees) and values appearances of love above the unseen reality of true inner love.
I agree with number 2's thorough answer. As humans, he hide behind our clothes. We rely on our clothes to help us "look the part" and feel it. This is especially true of royalty. The clothes become a costume hiding who we really are. I wonder if Shakespeare was not more aware of this as a writer of plays, since this is what happens every day on a stage.
By far the most significant image of clothing in this excellent tragedy comes in Act III scene 4, when Lear meets Poor Tom (who is Edgar disguised). Hearing Poor Tom's story and seeing him naked, Lear has his conception of what man is further challenged and realises that it is not all about wearing rich and opulent clothing, as his daughters do and he once did as part of his royal trappings. Note what he says in response to Poor Tom's speech about his life and its challenges:
Thou wert better in a grave than to answer with thy uncovered body this extremity of the skies. Is man no more than this?... Thou art the thing itself; unaccommodated man is no more but such a poor, bare, forked animal as thou art. Off, off, you lendings! Come, unbuttton here.
Lear seems to want to find out for himself if man is indeed "no more than this" by experiencing the same nudity as Poor Tom, trying to find out what the identity of humanity is all about. Stripping himself is an attempt to try and work out what real humanity is, without the fineries that characterise his daughters, and, as he has now realised, appearance.
Thus we can tie in the motif of clothing into the central theme of appearance vs. reality. Goneril and Regan, characterised by their fine clothes, are of course an example of appearance as they lie to their father to gain land. Poor Tom, Lear thinks, is true reality thanks to his nakedness that cannot be covered up. Sick of appearance, Lear seeks to experience reality for himself by taking off his clothes.