What is the relationship between the plot and subplot of King Lear?
Shakespeare's King Lear is not the story of a single man who is betrayed by his daughters but a story about the universal tragedy of old age--how one generation is inexorably replaced by the generation it created through love or lust and nourished until adulthood. That is why there are two plots. Lear has daughters, Gloucester has sons. Both men find themselves out in the cold, stripped of everything they used to own, including their titles. But this is a universal theme. It has been going on among us Homo sapiens for something like seven thousand generations. Shakespeare shows this happening to aristocrats because that was the tradition in drama--but it happens to everybody. Parents typically love their children, but children do not necessarily care about their parents after they themselves are grown up and have developed adult interests in survival and procreation. In Measure for Measure, the Duke disguised as a friar tells the condemned prisoner Claudio:
Friend hast thou none;
For thine own bowels, which do call thee sire,
The mere effusion of thy proper loins,
Do curse the gout, serpigo, and the rheum,
For ending thee no sooner. III.1
At least that was Shakespeare's view. Your own children can hardly wait to get rid of you and to get their hands on your property. This was certainly the attitude of Goneril and Regan with regard to their father Lear and the attitude of Edmund towards Gloucester.
Old age is also a time of regrets. This is symbolized by Lear's bitter regret that he disowned the one daughter who loved him in favor of the two who cared nothing about him. When he meets Cordelia again near Dover he tells her in a stunning metaphor:
You do me wrong to take me out o' the grave:
Thou art a soul in bliss; but I am bound
Upon a wheel of fire, that mine own tears
Do scald like molten lead. IV.7
This is a good description of the sufferings that go with old age.
What makes old age hard to bear is not the failing of one’s faculties, mental and physical, but the burden of one’s memories.
Gloucester feels exactly the same way about Edgar as Lear feels about Cordelia.
O dear son Edgar,
The food of thy abused father's wrath!
Might I but live to see thee in my touch,
I'ld say I had eyes again! IV,1
Both men's bitter regrets actually symbolize the regrets that all old people feel in old age. Gloucester disowned Edgar, the son who truly loves him, in favor of Edmund, the bastard son who cares nothing about him but only wants his lands and title.
The two old men are accidentally brought together in a pathetic scene in Act IV, Scene 6. They are hungry and dirty. They have been stripped of everything and are living on weeds and mice. Gloucester has even lost his sight. This great scene symbolizes the fate of every generation when it is no longer wanted and is only in the way. In giving Lear daughters and Gloucester sons, Shakespeare intended to represent the whole human race, each generation treading on the heels of the generation that came before it. The characters who love these old men--Cordelia, Edgar, and Kent--exist primarily to serve as contrasts to the ones who care nothing about them.
The subplot was probably also needed because the conflict between Lear and his two daughters had become static, a standoff. He is living in the wilds, and they had taken possession of everything he formerly owned. He refuses to go back to them under their terms, and they couldn't care less. Shakespeare may not have known where to go with that plot. Lear rages against his daughters, but he is helpless. His extreme rage is intended to explain why he doesn't just go back and live with them without his hundred knights. They would be glad to provide first-class shelter, since it must be an embarrassment to have their father wandering around in a condition worse than a beggar's. The introduction of the subplot renews dramatic interest, along with suggesting the universality of the theme.