For some reason, I thought you were going to Vienna (above post). But it seems you're going to Venice.



Those are your nonstop options on a random date in Nov (Nov14). On top of that, you have another 10 options with connecting flights (MUC, VIE, BRU, ZRH). As others have said, I wouldn't worry about missing your initial connection. You may be automatically rebooked, so just check your booking on the app. If not, any LH desk in FRA will be able to assist you. There is no need in trying to find someone from UA in FRA.
If you happen to fly Polaris, just head to the nearest LH lounge. Their service desk can assist you as well.

What I'll do with tight connections is to have a game plan. This means doing exactly as above - look at my options and sort them by departure time and availability. You can check the LH website for one-way flights from FRA-VCE for two in the morning of your departure day from the US. I also check FlightAware for historic data on my TATL flight. If it is mostly late, there's a good chance you'll miss the connection.

Judging by the info you provided you'll be on UA932 which arrives at 11:50, departing to VCE on LH328 at 12:50. You should definitely make the 16:50 flight (LH330). In case that would happen to me, I'll check whether LH330 still has availability upon arrival (or the morning of your departure) and then proceed to the LH desk asking you to rebook onto that flight. Otherwise, you run the risk of LH putting you onto the cheapest flight to them (which may well be the 21:10 one). Come prepared.

I know, TMI. But I hope you'll have a great time in Venice with your wife!