I not sure that MMB itineries ever accurately reflect lounge access - and may only reflect your original booking before the MFU.

If this is the case it is probably basing its info on the fact the domestic sector will be ticketed in J class (Biz UK) which gets lounge access and the WT+ sectors which don't).

Your MFU to Club will obviously give you access to the lounges at LHR no matter what the MMB screens say.