It was a couple of years ago since I did MUC-LHR with a buggy, but my recollection was the our buggy had to be given up at checkin to reappear at LHR. We were loaned small buggy at Checkin which we were able to take to the aircraft door but which never left the ground so we had to manage without on arrival at LHR.

As usual, the error(s) here are in providing accurate information.

I have also done MUC-LHR with Lufthansa and at the other terminal we were allowed to take our buggy through security (they swabbed it as it wasn't going to fit the scanner) and to the gate. Don't recall were we reclaimed it sorry