I'm pretty sure I'm reading it right, but I just want to confirm that regeneration can be activated in either player's states phase. So my Asawira can regenerate at the end of my turn or at the end of my opponent's turn. Also means that if my opponent makes him unconscious on their turn, he can regenerate in time to save me from Loss of Lieutenant.
While the Regeneration part of this question is right, the Loss of Lieutenant part isn't. There is nothing in the Cancellation section of the LoL rules that lets you re-activate your Lieutenant if you cancel the null/isolated state on them, which caused the LoL rule to go into effect.
But LoL is only checked for in the tactical phase. If your LT cops it in the enemy turn and regenereates in that turns states phase, he is alive and well for the check in the tactical phase of your active turn and you don't enter LoL, right?