What is the meaning of "nemesis"? How should I determine who might be the nemesis of King Lear? What exactly should I be looking for?
Wikipedia provides a full discussion of the term “nemesis,” but the short meaning of it is “your worst enemy.” Usually our worst enemy resembles us somewhat, and so is the case with nemesis. So, in trying to find this in King Lear, you need to ask yourself the question: who is Lear’s worst enemy yet also shares some of Lear’s characteristics. Perhaps it is his daughters Gonreil and Regan for they certainly work toward his demise—his own daughters become his enemies—yet in being his daughters they also share some of his characteristics. Even Lear himself comes to realize Gonreil behaves as a mirror image of himself in hr arbitrary exercise of authority: “But yet thou art my flesh, my blood, my daughter, / Or rather a disease that’s in my flesh / Which I must needs call mine” (2.2 410-12)
In your typical tragedy, the main character has a "tragic flaw" whic ultimately leads to his/her downfall. You could say that King Lear's worst enemy is himself. After all, it was his choice split the kingdom, banish Cordelia and Kent. In much of this play King Lear thinks people are hurting him much more than they are. Whose fault is that?
Cordelia loves her father the most but is not willing to exaggerate her speech like her sisters did. Lear is looking to be flattered. Kent, an advisor, advises the King on his actions and for speaking truth he is banished.
Later on in the show people do terrible offense to the King. They are perhaps enemies. But a nemesis is one who stands in the way of everything the character wants. Isn't Lear's inability to accept the truth standing in the way of his own happiness? By the time he realizes this it's too late.