I think the question is less about Lear as a character, and more about the play.
Despite the disorder, disruption and madness which pervades the play from the beginning, it is also full of portrayals of human constancy, forgiveness and loyalty. Nevertheless, having set up such positive moral values the ending of the play appears to shatter them. No wonder, perhaps, that some critics have argued that this is Shakespeare's most nihilistic play, insofar as it seems to confirm despair rather than hope. For Jan Kott, (Shakespeare Our Contemporary,1964) '...established values disintegrate. All that remains...is the earth, empty and bleeding.' Certainly, the representations of 'good' in this play have either to go in disguise (Kent, Edgar) or be banished (Cordelia), and while Kent and Edgar are survivors, they are not saviours. Edgar is hardly straightforward, either, having demonstrated a capacity for self-righteousnes and cruelty. And 'bad' Edmund's deathbed repentance is immediately dashed by the terrible stage direction: Enter Lear, with Cordelia [dead] in his arms.
Throughout the play's performance history, the bleakness of Shakespeare's ending has caused controversy, not least because it seems to deny the possibility of Christian redemption. From 1681 to 1823, the play was performed with a happy ending with Lear and Cordelia alive and reunited. The ending of the original version has prompted some critics to argue that Lear dies in ecstasy, with the illusion that Cordelia lives; others, of course point to the monstrous delusion, with the implication that the play's 'default' is despair, not only for parents and children, but for society (and thus justice, and morality) as a whole.
It is surely important that this play was written at a time when great orders are seen to collapse, chaos threatens, and that 'salvation', temporal or spiritual, is not an option if it depends on great orders. The view of God (or in the literal, pagan world of the play, the gods) is unconsoling: playing with humanity like little boys torturing flies (Gloucester, IV,i,36-7). The play's mythic quality plays on our sense of wanting a happy ending as in a fairy tale, or at least a morally satisfying one. Instead, we have a highly ambiguous ending at best, and one which must call the play's expectations into question.
The answer to this question is one which will be argued by critics throughout time. As with any text, the interpretation of the text is up for intense criticism, scrutiny, and differing views.
That being said, there are two main views on King Lear regarding Lear's death at the end of the play. Some critics, as stated, see Lear dying joyfully, while others see his death as one filled with anger and blindness.
As for the side in which Lear dies happily, one could support this view by interpreting Lear's holding of Cordelia as his final acceptance of his daughter. Cordelia refused to submit to her father's wishes (basically by refusing to tell him things which he wanted to hear). Goneril only wanted to please her father. Lear readily accepted her for that fact alone. It is not until Lear is holding Cordelia that he can have the relationship with her (for a very short time) that he always wished for. In this way, Lear is able to die happy given he finally has his daughter.
On the other hand, Lear feels responsible for the death of Cordelia. It is through his actions which led to the death of Cordelia and his recognition of that which forces him to see the truth behind her death which bring about his anger and blindness. Lear simply comes to terms with his part in Cordelia's death and his anger regarding it is finally revealed.
As for the blindness, Lear fails to see Goneril as the daughter who gave him everything. In this way, Lear dies blind to the love of Goneril. His desire for Cordelia's love forces him to be blind to his other daughter's love.