I would expect this combo would be easy to find on the airlines' own website, as they are alliance partners. United will have their own flight numbers for a Lufthansa flight, but in the flight details you can see a little "operated by Lufthansa" on it. Another giveaway is a very high flight number, usually between 7000 and 9000.
Also, check both airlines' websites for the same flights (the numbers will be different, but check by schedule) The flight costs can be very different.