We may say that Lear suffers to learn a lesson, as implied above. He has gone against his nature and the nature of kingship by abdicating his power. It was power that shielded him from the moral reality of the things he has done in his life. Without the crown, Lear can no longer justify his evil deeds.
It's interesting to consider whether or not Lear's action would have been evil, to him, had he maintained the throne. He may have died content, feeling morally clean.
Yes, it can be argued that Lear commits many "sins" that lead to his punishment. Additionally, because Lear is a play of the genre of a tragedy, it follows that it would be expected to adhere to the typical conventions of one. One such feature of a tragedy is that the protagonist has a hamartia (flaw in character) that leads to his suffering and subsequent downfall. So, Lear's suffering is also as a result of the play being a typical Jacobean tragedy.
Predominantly, this flaw in character is his act of hubris against the gods. He divides the kingdom, which in Jacobean times, would have been understood to be an act of rebellion against the divinely inspired Great Chain of Being. When Lear claims he will do this to "avoid future strife" there is dramatic irony in this; we as an audience know that dividing the kingdom will only bring more disruption.