No, new historicism is about how all individuals (including Lear) who step out of their state-sanctioned role pay heavily for it. The state hierarchy is beyond any person's control (and this links up directly with the Elizabethan's belief in the "Chain of Being" - a hierarchy not even under the king's control but God's). Consider this:
- Lear as king has a responsibility to maintain stability. When he divides the kingdom, he causes instability. He dies.
- Cordelia fails to carry out her role as a subject and as a daughter when she refuses to participate in the love test. She dies.
- Gonerill and Regan usurp the throne and do all sorts of mean things. They die.
- Edmond does the same. He dies.
On the other hand:
- Edgar maintains his integrity throughout the play (although he has to resort to subterfuge, this is only because the order has been turned upside-down). He survives and is rewarded with kingship.
- Albany, although somewhat henpecked at the beginning, asserts authority over Gonerill and Regan and brings Edmond to account for his actions. He survives.
- Kent is loyal to Lear to the end, even when he is banished and undergoes a lot of suffering to serve his master. He survives.
A new historicist reading would sympathise somewhat with Gonerill, Regan and Edmond, traditionally damned characters, because the state-sanctioned order precludes them from getting power in any other way (although it would not openly support what they did).
Hope that helps