Here's the scenario:
I play Lighthouse.
On the next turn, my opponent (for simplicity, it's a 2p game) plays Corsair.
On my next turn, I play an Outpost, so I get another turn.
Question 1: Do I ignore the Corsair on my first turn after it's played, even though the Lighthouse has "expired"? Answer seems to me to be a pretty clear yes; it's official (even on the wiki page for Lighthouse) that the Lighthouse needs to be in play when the attack card is played in order to be effect, and this would just be the flip side of that.
Question 2: Do I ignore the Corsair on my second turn after it's played? Still seems like a pretty clear yes, by the same token.
Question 3, and this is where it gets interesting: When do I discard the Lighthouse from play? Does protecting me from the Corsair count as "something to do" on the second turn after the Corsair is played, causing the Lighthouse (as a Duration card) to stay in play, or has it already "done" everything when the Corsair was played, meaning that it's discarded at the end of the turn it gives the second coin (i.e. the first turn after the Corsair is played)?