Originally Posted by NewbieRunner

Your flight from MAN will usually park at a remote apron position and you will be bused to international arrivals B. You'll have to go up to passport control, through security and walk to your departure gate almost certainly through the tunnel.

This is a legal connection and should you miss your connecting flight LH will put you on the next available flight. By what time do you have to be in Rome? Depending on the latest time you must be in Rome, I might try and book an alternative fight. Sometimes FRA sends a bus to take connecting passengers directly to their flight and I have certainly seen this happen to flights from MAN (and the flight wasn't even late), but there's no guarantee this will happen.