I suggest you post your message on the LH board as this is more to do with LH than Mexicana.
Why aren't you going on the direct nonstop LH flights to FRA from either Dallas Fort Worth (DFW) (only 183 miles from AUS) or Houston (IAH) (just 148 miles from AUS)? I know that UA does not connect direct to either, but it would be surely worth going on AA/ Delta (1 hr to DFW) or Continental (47 mins to IAH) to avoid the schlepp to ORD.