Re-routing definitely means paying the fee. But, there may be some cases, when you are able to avoid paying for it. specially when it involves same airline and connecting sectors for which direct flights exists.

If you want to do do LAX-MUC, instead of LAX-xFRA-MUC, then your best bet is to get to the airport on the day of the flight and talk to the airline. If the direct flight is around the same time as the other flight, then it probably will be easier. Of course, I am also assuming that all flights are LH.

In that case, the airline in question will just give you a single boarding pass against two ticket coupons. Re-routing and re-issue is not involved. I have done this once. I have also once actually introduced a connection (MAN-FRA-MUC), instead of MAN-MUC without paying for it, by just arriving at the airport a way too early and make a nice request to LH (handled by BD, i think).

The airline making time changes would be a perfectly good reason to go talk about it, specially if it makes your connection time really tight at the connection point. It may actually make your connection time illegal, in which case the Airline will be requried to offer re-routes. Some airports like LAX now have huge MCTs on domestic-international flights (3 hrs i am told), so that may be of advantage to you.

good luck.