Originally Posted by JJeffrey

There really isn't much else to ponder, as noted above you'll arrive into T3, just follow purple signs to flight connections and take the bus to T5, clear security then head to one of the 2 BA business lounges in T5A.

LHR-BSL will almost assuredly depart from T5A; all T5A gates are at most a 5-6 min walk from either of the lounges there. On the off chance it departs from T5B or C then just take the elevators down to the bottom and walk over in the tunnel if you like walking (that's what I always do for T5B/C departures).