This is an easy call: Bench your goalies.

You can't allow yourself to worry about an unlikely situation.
The odds of Luongo getting a shutout are probably 1 in 10 anyways (10 SO every 100 starts).

But the odds of Lundqvist having a bad game and you LOSING two categories is possible.
Even Lundqvist has a bad game every four games.

If this "event" was run 100 times, you are going to win GAA/SV% probably 80-90 times if you simply bench Lundqvist.
You have to play the odds.

More importantly, the STL @ VAN game is at 9:00pm.
So your opponent gets to make a later decisison with his goalie (Luongo, assuming this is "daily starts").

NYR plays at 6pm.
If Lundqvist shits the bed, you may be losing in GAA/SV% when the VAN game starts.
He simply has to BENCH Luongo and he wins two categories.

Bench 'em.