Two of us will be travelling from Lyon to Munich in mid-April, 2014. Train or plane? An alternative is Valence, France to Munich if the train works.
There is a French TGV from Lyon to Karlsruhe, Germany. From there you can take one or two German trains to Munich. Depending on the date, there are advance purchase Europa-Spezial tickets available from the Bahn website. I saw 89€ fares for some days in April. The trip takes a little over 8 hours.
Lufthansa flies direct from Lyon to Munich in less than 90 minutes flight time. I'd pick that over an eight-hour train trip despite the hanging around.