Since the lack of equilibrium on the baggage interline seems to exist only WS-->LA I am sure returning from Lima will be a non-issue as well.

But because your WS was also an codeshare with LA it did seem improbable they'd have said no on your outbound. How mean would that be, really?

It is quite common to see these pricing differentials despite codeshares on the same aircraft, e.g. your WS segment was a better price than a LA deal. Sometimes it's the other way around.