The Lannisport card says that I can claim one power (after winning a intrigue chalenge) paying one gold, and if a have 2 Lannisport in play, can I pay 2 gold to claim 2 power per intrigue challenge?

Well, Lannisport is unique, so I'm not sure how you are planning to get a second copy into play….

But in general, if you have two non-unique cards with the same title that both have general, non self-referencing Response effects, you can trigger each one separately when whatever they are Responding to happens.

tnkz, I totally forgot that.