Can use the Gift to Lower Baratheon Character who has Night's Watch trait from The Wall?

Kuba said:

Nope. Unless otherwise stated, cards in play won't effect the traits/abilities of cards in your hand, as they're not considered to be in play. One of the few exceptions I can think of is Tyrion's Revenge from AHoTa. And it has to specifically reference that Clansmen characters in play as well as in your hand gain the Lannister affiliation.