I'm not sure I understand what you are doing? You are arriving into MUC on BA in CE, then have another flight on BA a few hours later? Back to LHR? The BA lounge in MUC is completely forgettable (and you won't have access to it on arrival). You could go to the AirBräu restaurant, but that won't keep you busy for more than an hour. Or you could go to the visitor's park, that's about it.