Would there have been a direct connection between MUC and FRA after your arrival in MUC? If not, they may have considered your flights to happen on the same day (as you wouldn't have had the chance to continue your journey within the given timeframe). I guess that this would be the same if you arrived on LH F in FRA at, let's say 11:30pm while continuing at 04:00am on the next day (yes, I know that's not too realistic) - they would have to let you in at 11:30pm and probably wouldn't throw you out at midnight.
In some instances, LH lounge staff seem to be quite obliging. When I arrived in FRA coming in from JFK in LH F and the Fraport staff gave me wrong directions towards the lounge, the arrival lounge dragon organized FCT access for me, although I didn't have any connecting flights.