I'm unable to find Lufthansa First class inventory when trying to book via United.com. There is on Google Flights as well as on the LH website. Is this a temp. issue or a glitch in the system (because of conflicting fare class A with LH First and UA E+)?
United-marketed LH flights (codeshares) do not have First inventory, which is probably your issue. If you need it plated 016, you should probably be able to call United and spell out the segments with the LH flight numbers.