I wasn't suggesting they SHOULD. I was just wondering why they hadn't like Skyteam did in T4.
Star Alliance had a single lounge at T1 when it occupied it (and only half of the Star Alliance was at T1) and its airlines chose to have three separate ones when they were unified into the new T2. Besides LH which monopolised the main terminal lounge (and so is the lounge for almost all short haul *A flights), SQ, AC and UA all wanted their own spaces because LHR is such a critical hub for their operations. Hardly surprising BA has lounges at T3 given the amount of operations there, but again AA and CX regard LHR to be a key premium location for their operations (in competition with UA and SQ no less), and QF took the opportunity to use the ex. SK lounge site to lure OWS/E cardholders to its space as well as saving on most of its premium passengers using competitors' lounges. JL had a lounge at T3 at one time too.