Miles & More (Lufthansa, Austrian, Swiss, and other partners) - M&M Upgrade

On my retourn flight from LAX to FRA (UA-ticket, operated by LH) I would appreciate take a nap in Business-Class.

Is it possible to be upgraded redeeming LH M&M miles? (I do not hold any UA-miles)

As a LH M&M member of any tier you should be able to upgrade with miles on Lufthansa metal regardless of who your ticket was bought from.

If it is a codeshare flight, it cannot be done in advance, but will probably work at the airport, if you have an upgrade voucher from M&M.