Since your connection time is 4:25, it may be interesting to attempt transit. You are flying LH-F and connecting to TG-C all *A on the same ticket. Perhaps one can put in the record the need for a transit service/ escort at BOM. If you can let BOM/LH and BOM/TG station managers be in the know, it couldn't hurt either. Hopefully your escort will be there waiting with TG-C boarding pass!

There is the tricky issue of notifying Indian immigration/ customs authorities. It seems they need to be informed well in advance of flight arrival (LH-F) of the details of the transit passenger and permission sought. This leads to informing transit security; there are different stamps they use to mark the TG-C boarding pass.

I wish you a pleasant adventure; perhaps a good way to kill 4 hours