During the dark days between the SR grounding and the LH takeover, LX sold a number of their LHR slots to BA to generate some cash (thinking back then that they would soon be a member of oneworld). LX currently does not have enough LHR slots to maintain a meaningful operation on both the ZRH-LHR-ZRH route and GVA-LHR-GVA route, so they choose to focus on their main hub. Perhaps GVA-LHR-GVA will return at some point if LH decides to dismantle bmi and redistribute their slots, or some other option will turn up for LX to acquire more slots, but until then it probably will not happen.

However, LH did mention recently that they were considering re-building the bmi European network, so perhaps we'll see bmi service with LX codeshares on LHR-GVA-LHR at some point in the future.

Oh, and about that Geneva to London traffic - I would bet that a lot of the high-fare business traffic is actually pretty happy about flying into LCY instead of LHR, because they also cannot imagine crossing the whole city (in the other direction).