Several elements of Lear's character seem interesting to consider in a psychological framework. His great pride leads him to deny certain realities and even to insist that these realities be changed to better accord with his pleasure. This is hubris bordering on pathology.
Lear also proves himself to be quite stubborn - to the point where he risks illness by staying out in a storm instead of asking for help. This reckless behavior would be interesting to investigate psychologically.
In assessing Lear's psychological makeup, I think that one has to examine a type of "mid- life" crisis that he undergoes later on in life. He is older than middle age, but I think that the he is at a point where there is some level of questioning about the world and his place within it. This unsettled feeling is enhanced by the children's responses to him, and the fact that what he once believed to be true is unreal and what was considered unreal is the most lasting. Lear's psychology is one where a struggle to determine what constitutes "real" and "unreal" forces him to doubt all that is around him in the world. This foray into his own state of being is terrifying and one where a pure reflection about his own place in the world and what he believes to be true becomes part of the central focus of the drama. In this light, Lear's psychology is one that experiences great growth in understanding that what was once seen as true was actually false and what was actually false was actually true.