LX23 JFK-GVA is showing as an A333 and this Swiss forum thread suggests to me that that means new business. LX15 and LX17 are showing as A343, which I believe means old -- although the Swiss thread suggests that LX15 is, at least sometimes, operated using an A333 with new business.

As to whether to book or wait, only you know how important the trip is and how much you're prepared to risk not getting a seat in C. If it was me, and if flying a day early was fine, then I'd book the LX new C product like a shot.