A tragic hero is a protagonist that has a fatal (tragic) flaw; usually, the audience finds sympathy with the hero.
At the beginning of the play, Lear seems like a fine ruler and in his generosity, he decides to divide his kingdom equally among his daughters. But then he encourages his daughters to compete by pledging their love for him. When Cordelia refuses to make overly dramatic praises, as her sisters do, Lear's pride takes over and he essentially disowns her and then banishes her.
The barbarous Scythian,
Or he that makes his generation messes
To gorge his appetite, shall to my bosom
Be as well neighboured, pitied, and relieved
As thou, my sometime daughter. (I.i.114-18)
(The "barbarous Scythian" was a savage nomad and "makes his generation messes" refers to making a meal (eating) of parents or children. Here, Lear says that he will treat Cordelia as he would those who would commit these savage acts; his pride clearly overreacting.)
Thus, Lear's first tragic flaw is pride. And this leads to his downfall. Had he put his pride aside, he might have recognized that Regan and Goneril were buttering him up while Cordelia was speaking the truth without the superfluous praises.
Lear's second flaw is his "blindness." He can not "see" that his eldest daughters are being false and he can not see that his youngest is being truthful by refusing to make a scene in pledging her love to him.
Lear's descent into madness stems from his pride and inability to see things clearly. He also is unable to cope with his new role as retired king. He wants the authorities of being king but does not want the responsibilities. His eldest daughters eventually usurp his authority. They do so greedily and dispassionately, but Lear did bequeath his kingdom to them. Unable to cope with his conflicting role of being king and not being king (having the prestige but not the responsibility), Lear loses touch with reality.
The question is, should the audience be sympathetic to Lear. Since he was initially benevolent in dividing his kingdom, he seems like a fair and generous ruler. Therefore, his fall seems all the more dramatic and tragic. His flaws do contribute to his fall, but he is also manipulated by his daughters and the circumstances. So, there are reasons to fault Lear and reasons to be sympathetic to him. Aristotle thought that the tragic hero had to be "blameless" so this would not qualify Lear as a tragic hero. But if we stretch the definition, saying Lear was only partially to blame, he can be considered a tragic hero (using this more sympathetic definition of a "relatively blameless" man who has flaws and is the victim of others' greed and other circumstances.)
King Lear is a tragic hero.In the beginning, he rules with mighty but when he divides his kingdom and deprives Cordelia of her share ,he seems to be a great cruel.Afterwards,the reaction of his daughters really suffer him a lot. His condition,becoming mad ,the death of Cordelia and at last his death really wins sympathies from the audience and we can call him a tragic hero.
The tragedy of King Lear is because of his inability to recognize reality, or to see things for what they really are. It is ironic that he believes Goneril's and Regan's lies about their love for him; while he falsely accuses Cordelia of being disloyal, when in fact, she turns out to be the only one of the three who loves him.