My recommendations of the lounges I have experience of:
LHR-PHX in PE on BA: You can access any of the OW business class lounges in LHR T3. The Cathay business lounge is probably your best option.
PHX-SJC in Y on AA: A perfectly acceptable, albeit standard, AAdmirals Club at PHX. Fine for a quick pit stop, but could get a little dull for your 3-hour layover.
LAX-LHR in PE on BA: Either the OneWorld Business Lounge in TBIT or the AA Flagship Lounge in T4.
LHR-MAN in ET on BA: Any of the three Galleries Club lounges in T5. T5B is best if there is time/you have the inclination to walk back through the tunnel to T5A. If not I would tend towards Galleries South for pre-6pm departures, Galleries North for later departures when it's quieter.