Not convinced that LH would do LPL-LHR, maybe LPL-FRA i.e. to their hub, but if KL can't make LPL-AMS work......
Can't see any overseas EU carriers doing LPL-LHR at present, IF there was to be one, would except it to be EI (currently on LHR-BFS), but don't hold your breath.
Yes there is a good fast (weekday) hourly London-Liverpool train service which is fantastic for those travelling city-centre to city-centre. For others the 2h15 journey can become 4h15. Timewise, at 4 hours plus, air becomes a very viable alternative, it's the same as LHR-MAN. Like everything else, it's good to have alternatives, but the operators have to be able to make it pay. Regretably, at present they can't.