If you're referencing THE CLUB at Phoenix (I don't believe there is an actual BA Lounge at PHX), access is for BA customers only (F, J, Sapphire, or Emerald), or for $ (everyone else). I'd guess you didn't have a BA issued "single" through ticket (PHX-LAS-LHR). If it was instead an AA issued one (single through - no stopover), the matter is somewhat grey. This is only a guess. Let us know how this is resolved.