OP seemed to have an award ticket booked on UA LAX-FRA connecting to LH FRA-VIE. The LH segment was cancelled. I'm guessing that this was booked with UA miles. Is this correct?

OP needs to do some research to find possible flight numbers on which tickets in the same cabin are still being sold. Write down flight numbers and specific times (and dates) to tell the phone agent when you call. Decide what you want and ask for it, don't vaguely ask the agent to find something for you as they will probably offer only one choice, the one that would be easiest for them. If you're willing to stay overnight at FRA or MUC, possibly at your own expense, there might be more choices. I'm not sure whether LH duty o care would apply for hotel and meals.

Since it's an award ticket, UA can open award inventory on flights operated by UA but must use available partner award inventory on LH and other partners. IIRC UA can request (through some partner liaison desk) that close partners such as LH open award inventory, especially since this was LH's fault. Changes must be made through UA and the ticket must be reissued promptly after a phone agent rebooks it. [Check that you get a receipt with a new ticket number. This is important.]

Surely there are other connecting flights from FRA to VIE on the same day. Alternatively, look at connections through MUC, using UA flights (remember, UA can open award inventory for you--you might need to remind the agent of that) for the transAtlantic portion and any needed USA domestic connecting flights. LH should have multiple daily flights from MUC to VIE.

As others have said, file the EC261 claim with LH after the travel. There's a big sticky thread in the BA forum that's incredibly useful for understanding the EC261 rules.

If this doesn't work, taking the train from Munich is also a possibility. IIRC it's about four hours and quite scenic. The train trip from FRA would be too long after a long flight IMO.