The F-35 is, first and foremost, an attack and electronic warfare platform (F- or B-designation irrelevant to the Americans, who chose the designation - witness F-105).
Surely in UK service it'll simply be
Lightning FGR1, with any subsequent post in-service tweaks resulting in an
FGR1A or
FGR2 designator?
As for choice of squadron, perhaps some wag in the MoD simply thought the 617 badge might be appropriate for the type. The boys in the paint shop have been getting in enough practice after all...