We do get a few hints in "Franny" that she and Lane are in fact sleeping together. First is Franny's P.S. in her letter that she "spoke to Mother on the phone last night" and that Lane should "relax about that Friday night" because she doesn't "even think they heard us come in" (Franny.1.5). Later, Lane talks about sneaking in to see Franny that night. And finally, after Franny has collapsed in the restaurant, Lane asks her: "You know how long it's been? […] When was that Friday night? Way the hell early last month, wasn't it? […] That's no good. Too goddam long between drinks. To put it crassly" (Franny.5.16).
So we can fairly safely conclude that Franny and Lane are sleeping together. What's interesting to consider from here is the rather unpopular theory that Franny is pregnant – that's why she collapses, the theory goes, and why she feels nauseous and won't eat, and her whole spiritual crisis is just a mask for her pregnancy. (Read about it in "Holden At Fifty.) You won't find too many readers or critics that buy into this theory, but you can keep it in mind.