Welcome to FT, fivefortysix!
If you intend to take a later flight, give LX a call (or your travel agent, or whoever issued your ticket) and ask them if you can change your reservation to the next day ZRH-LAX flight and have a stopover in ZRH. @:-)
To just not show up and hope to get your way by telling some story is about the worst way to go about this...
Seriously.