This may sound too basic, but have you looked into one way business class tickets? In the limited amount of paid business class I've done, I've often found that one way tickets are approx 1/2 the round trip price. If you are planning on throwing away the return of two round trips, perhaps booking a one way for part of the journey would save even more money.

Depending on where your final destination is (and how price sensitive you are), it may also make sense to look at flights into Geneva. A quick search on Kayak for some random dates (without a Sat night stay) at the beginning of August showed about $4300 all in. That should be lower than 2 RTs to Lyon.