Can you check through your bags to the final destination if you're on 2 separate reservations and carriers?
@bucketlist, did you eventually get your bags back?
@zappa42m - if UA is late getting you to MUC, tough luck. They won't do anything for you for your completely unrelated reservation on a different carrier. If they're contracted to get you to MUC and they do that, end of story for them. You'll have to deal with LH for the MUC-DUS segment separately if you miss that connection. People miss flights all the time, even the super-punctual Germans (hooray for stereotypes!). I'd read up on LH missed flight policies.