Can repeated game sustain a discounted average payoff that is not individually rational?
I'm inclined to say $(2,2)$ is not sustainable, though I don't have a formal proof at the moment. 

To achieve an average payoff of $(2,2)$, the players must play $(H,H)$ in some stages. But then a player can deviate to playing $L$ and avoid any subsequent punishments by ensuring that he can always get at least $3$, which is better than $2$.