If there's a queue at customs don't feel you have to join it, just don't make eye contact and continue walking between the X-ray machines. Works every time for me.

On departure from KUL you are entitled to use the lounge shortly after immigration, they always try to send you off to the main lounge in the satellite terminal, but the smaller lounge in the main terminal is a bit more intimate.

My biggest problem with BA on this route is the 3hr checkin rule at the end of a long week on the return leg. You check out the hotel in the morning, finish your meeting at 5pm then get the cab to the airport. Then you're stuck waiting a couple of hours for checkin to open to gain access to the lounge and showers. I know a lot of people say don't head to the airport early, but when working on the outskirts of KL there's not necessarily anything else to do but go to the airport. MH cater much better in this respect allowing you to check in any time, and also having in town checkin at KL Sentral so you can drop your bags in the morning, have your meetings, then get the train. BA seem too cheap to pay for this facility.

A general tip for KL, get the GrabTaxi app. It makes dealing with the drivers much easier and they won't rip you off.