Literary traditions: kings and clowns
What kind of tragedy is Lear? Like the hero in classical tragedy* he falls partly from pride (hubris); like a medieval tragedy Fortune's wheel turns, Lear falling from power to poverty and madness.
But what kind of tragedy includes a Fool?--especially since none of Shakespeare's sources, historical or literary, mention him. One of the earliest English tragedies, Gorboduc, had a plot similar to Lear: an old king divides his kingdom between two sons (Ferrex and Porrex), and the result is civil war and death--but there is no Fool. Sir Philip Sidney disapproved of "mingling kings and clowns" in plays of any kind.
Was Shakespeare satisfied with his play? There is some evidence that he may have revised it after its first production. It is one of the major puzzles of the texts of his plays that King Lear survives in two markedly different versions.
Footnotes
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Kent the chorus
There is at least one other way in which Lear follows the tradition of classical tragedy: Kent can be seen as a "chorus" figure.
(Click for classical tragedy.)