You might also consider the idea of "nature" or what is "natural."  Shakespeare delves into the core of what it means to be human and what eminent laws should govern one's actions in a world beset by compulsions like lust, greed, and jealousy. 

For example, in both Lear and Caesar, people who should be loyal betray those they should "naturally" be loyal to (a father and a ruler).  As a result, they are "punished" for breaking the laws of humanity and of men.  Such actions are reflected in the surrounding environment; therefore, these betrayals in the world of men are also seen as disturbances in the natural world as well (horrible storms, omens, a pervasive mood of dread, the appearance of ghosts, ironic role reversals, or madness).   

In essence, Shakespeare sought to affirm societal values--ones which would seem to support the status quo and support a certain degree of conformity.  In both plays, you can see Shakespeare's support for the Divine Right of Kings with Caesar and Lear both playing the role of king.  Not only is Lear a ruler, he is also a father--the "king" of his family.  When both Caesar and Lear are removed from power, the natural world becomes topsy turvy.  Lear's daughters (except for Cordelia) become villains because they perform the most unnatural act of all--betrayal of one's father.