Professor Lake

What happens if I play a Neutral card with
Professor Lake (Forgotten Lore F3) out?

Professor Lake reads, “Forced Response:
After a player plays a card, until the end
of the phase that player can only play
cards that belong to a different faction
than that card.” Neutral cards belong
to no faction so any card with a faction
would qualify as a card of a different
faction. You could not play another
neutral card however since the result
returned by the check would be identical,
of no faction, and hence could not be
of a different faction. The neutral card
must be played first for the same reason,
if I played a Miskatonic card first, a
neutral card would not be able to return
a check of a different faction (as no
faction is not a faction, and therefore not
a different faction), so would be illegal
to play.