Hopefully we will call it the Lightning FGR mk1. None of this US F-35 nonsense, and there is no tradition of using a 'II' designator when we re-use a name (in the case of the UK the Lightning would be III anyway) - e.g. Tornado, Typhoon, Fury, Tutor etc
In the same way the MFTS T-6s should be Harvard Tmk1.