Salinger is creating a character by having him say 'laying' instead of the grammatically correct 'lying'. Many native speakers confuse these verbs, and someday they may both be acceptable in formal English in this situation. Now 'lay' is not.
You must not think that every statement that authors write is grammatically correct. They may introduce errors on purpose. You have to consider that the author of a work of fiction is not necessarily always writing as himself. That is, he is not using his own grammar, but the grammar that his character would have used. The character who is the referent of "I" is the character whose grammar Sal