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.