If Corse Lake leaves play and then re-enters play, I take it that any power claimed via the first Corpse Lake no longer counts re the limit

e.g.

• I have Corpse Lake in play and use it to claim 3 power prior to the marshalling phase
• During marshalling another card affect causes Corpse Lake to leave play (discarded)
• I then put another copy of Corpse Lake in play
• I now expect to be able to use it claim another 3 power during the round

You're correct HastAttack.

The only times the limit is not reset is when the cards own effect is what caused it to leave play and it has it's own built-in limit on it(See Ser Preston Greenfield) or if it's an event card.

From FAQ section 4.22 on Phase and Round limits:

( 4.22) Phase and Round Limits

A limit on an effect on a card that remains in play through the resolution of the effect applies to the copy of the card on which the limit is printed.

So yes, different card, different limit calculation.