You get lounge access at LHR as you are arriving on a long haul Club World flight. It doesn't matter what class he domestic is booked into. Just show your CW boarding pass at the lounge.
If you have time to kill, go landside, use the arrivals lounge (assuming you arrive before it closes at 14.00) , then through security and try out Galleries South. Then wander to the other end of the terminal and try galleries North.
Then write an account of how you got on, on here.