My bets on possible solutions:
Destroy the dementor (not terribly smart, but given the stress. . .) or do something else ‘impossible’.
Start talking about Voldemort being behind things. (This would be a pretty good distraction in the books. Less so here, though.)
Challenge Lucius to a duel.
Work out that Lucius thinks he is Voldemort and use that to manipulate him.
All of these look pretty obvious, though. I expect something a little more unexpected (possibly including there not being a solution).
My bets on possible solutions:
Destroy the dementor (not terribly smart, but given the stress. . .) or do something else ‘impossible’.
Start talking about Voldemort being behind things. (This would be a pretty good distraction in the books. Less so here, though.)
Challenge Lucius to a duel.
Work out that Lucius thinks he is Voldemort and use that to manipulate him.
All of these look pretty obvious, though. I expect something a little more unexpected (possibly including there not being a solution).