The problem is the meaning of "after executing a green maneuver". There's no other indication of what the timing of the ability is, and free actions are explicitly allowed to occur outside the Perform Action step.
If "after" means "at any point between the trigger and the end of the ship's activation", Night Beast gets his free Focus. If "execute a maneuver" means "the stuff you do during the activation phase that isn't Perform Action", Night Beast gets his free Focus. The rules are not particularly clear about what either of those terms mean--and, in several places, appears to use them to mean slghtly different things. Furthermore, the intent of the rules seems to be that you get to perform actions normally on rounds where you shed your stress token with a green maneuver.
Accordingly, I think Night Beast ought to get his free Focus in such a turn.
There is a valid reading of the rules, however, that says Night Beast must take his free Focus during the "Execute Maneuver" step of the activation phase. (If you're executing a green maneuver, after all, it makes sense to "locate" that activity in the "Execute Maneuver" step.) Since that step comes before the "Check Stress" step, Night Beast still has a stress token when it occurs, and therefore cannot take any actions, including free actions.
I disagree with that interpretation, but it's actually more straightforward than the others. If my wife says "After you go to the grocery store, could you stop and pick up that package from the post office?" she probably doesn't mean after I go to the grocery store, drive home, put the groceries away, eat a sandwich, take a nap, and check my RSS feed--she means after the grocery store but before I do anything else.
I think the wording of "after executing a green maneuver" is sorely in need of clarification, since it appears in multiple places and isn't very clear. R2-D2 can't cause this kind of problem, and I have a hard time thinking of how Lando's could, but it remains that "after [trigger]" needs an unambiguous definition.