We had a similar connection (LAX-LHR-DXB) last year - myself, mrs alect, and mini-alect (18 mths at the time).

We managed fine to go landside, HEX into town, walk around (Hyde Park) and grab some coffee, and could have spent more time was it not for the weather. We got back to T4, and mrs alect was even lucky enough to score a massage at Molton Brown (they only had one spot and I was a gentleman) and we all showered.

Very doable. No lounge (with the exception of the WING/PIER or the FRA FCT, and if you're wanting to bathe and sleep) is worth 8-9 hours.