Lufthansa generally doesn’t release first class award space to partners until 14 days out, but it seems there is availability on some routes to/from Munich in advance. Through September, there is some availability on routes between Munich and Washington DC, Chicago, Charlotte and a few other cities.
You can use United.com to search for flights. Simply select the cities you are searching and check the box for nonstop flights only. I was able to find first class availability without having to look too hard.
For more info and ideas for possible routings, see this View from the Wing post.
Last updated on December 20th, 2018