Used the new Turkish lounge in Nairobi the other day, and thought it was OK. Got there just after the majority of LH passengers had left (c2200 ish) and it was fine, with lots of empty seats. I guess getting there before most of the LH and EK (?) passengers would work as well.
As for the walk, it's no big deal, as going to any of the cafes airside involves a fair walk from check-in and to gate 10... And you don't need a lounge invite - just the boarding card is fine. I've tried to attach a few photos below of the lounge entrance, for posterity. Sorry if they're too big! Note BA isn't listed outside the lounge as being entitled to use it, and it sounds like the check in staff weren't exactly proactive in letting customers know.
For reference, since I haven't seen it mentioned before, BA have an early check-in (2-3 desks open) from 1930, then main check-in opens at 2130 (this for the W17 schedule where the flight leaves at 0030).
Should you arrive before 1930, there are now also a couple of OK coffee/snack/dining/WiFi options landside at the terminals themselves (no need to go to the Ole Sereni any more). Nicest one I saw was the Paul Caffe coffee bar/pizza/snack cafe outside at the very beginning of T1A (KQ/KL), from where it's only a minute's walk to T1B when BA opens its doors.
Oh, and mobile boarding passes are now accepted as well!
