The Genie was considered for arming the Lightning with the US providing the missiles and the UK the exploding bit. Proposal was for just one to be carried on the aircraft which might have been the T4 version rather than the single seaters as this met the two man rule regarding handling nuclear weapons.
The idea seems to have been dropped on cost grounds and also that the US would retain control / supply of the weapon and also whether the UK had the capacity to produce the nuclear warheads..