The key error of King Lear's kingship is that he does nor respect the necessary connection between power and authority—true or false?

I would say this is true.
Lear's problem (or at least, one of his problems) is that he wants to give up the "business" of being king while also keeping his power to have everyone bow to his every whim. He thinks even after he abdicates to his two older daughters he will still have the power to make others do as he pleases, not realizing that by giving up the authority of his political station, he is also forfeiting his power. He wants the best of both worlds and instead ends up receiving nothing but contempt and grief.
Lear has been a poor father and this backfires on him when he no longer has royal authority over his children. They are able to treat him poorly once he gives up his powers and by being brought low, Lear comes to a better understanding of how he has failed as a father and as a king.