Much like Shakespeare's famous history plays, King Lear offers a meditation on kingship and power or, more accurately, the loss of power. After retiring and divvying up his kingdom among his ungrateful daughters, Lear discovers what it's like to lose the power and authority that come with the responsibilities of active rule. In addition to being a monarch, King Lear is also a family patriarch and Shakespeare asks us to consider the similarities between a father's relationship with his children and a king's relationship with his subjects.
Although King Lear sets out to avoid family and political conflict, his decision to retire and divide his kingdom results in a major family conflict as well as a full-blown national crisis.
Without the title of "king," Lear's authority means ultimately nothing – Shakespeare's play, then, suggests that a monarch's power is completely arbitrary.