There are lots of flights between FRA and VIE. If you've booked on one ticket and UA causes you to miss your connection, they are responsible for rebooking you. However, at a large partner hub like FRA, LH will often take care of the rebooking for them. If you miss your connection, LH usually just puts you on the next flight automatically.

Note that you will probably be on Austrian Airlines, not Lufthansa, but Austrian is part of the Lufthansa Group.