It doesn't have to lose any energy at all (and in fact
doesn't--orbital motion is conservative). All it has to do is
increase the eccentricity to the point at which perilune goes below
the lunar surface (or just a mountain).

But would this **always** happen if a LM were left in orbit?

It depends on how low an orbit it is. The LM was sufficiently low
that, yes, it would *always* happen over time.

What's the lowest orbitting satellite of the moon right now? Are
there any that are expected to basically orbit the moon forever?


How low can an orbit be around the moon and expect not to crash onto
the moon?