Few things. To enter the airport building you need to go through security which can be long. 10 minutes is the average but can be longer. Inside the terminal there is almost nothing so don’t arrive to early. You will need to go to the check in desk even if you have hand bang only as you will need a paper ticket. If you flying Club then you can use the fast track security which usually empty. The lounge BA uses is near gate 2. BA usually using Gate 1 so basically next to it. The lounge is one of the worst you can have if I were you spend more time at the Starbucks. If you have priority pass then you can use the other lounge which is marginally better.
Don’t forget that there is a gate security for the BA flight which is random. If you pulled over then you will have to empty all your bag contents, etc and it will take anything from 5-15 minutes. So if you leave the lounge when boarding starting and you get pulled over for this security then you will board last. Boarding otherwise quite fast as RAK using both front and back steps. So usually they start boarding Group 1 then Group 7-9 and last the middle. If you want to board first then you have to get to the gate super early.