I think LCY's appeal is primarily its convenience and proximity to the City. Think I would choose LHR too, as I'm not City based, but have been very pleased with the EDI-LCY services I have taken. At peak times LCY fares can be higher than LHR and imagine that it's quite a profitable operation and their is little incentive for BA to build a lounge (if the airport authority allowed).

I've seen reports that CityJet struggle a bit and wondered if BA was to ever become more dominant, might a lounge appear. But suspect not as I presume most LCY passengers have a SC or GC and they seem to be able to fill the planes anyway.