LH Z fares are upgradeable using SWU's...so contact UA and get the paper versions so you can try. It's nice that LH allows you to upgrade from Z... UA does not on its own metal.

From what I understand from reading here LH does not cater for a full first class cabin on every flight if it is lightly booked. So when using a SWU it's best to contact LH the day/night before and let them know you plan to upgrade to F at the airport. They can be sure the flight has enough catering... otherwise, they can shut off the cabin to further upgrades.