Question

Does a lever always do as much work on the load as you do on the lever?

Answer 1

Ignoring friction, air resistance etc. ... yes.

By the Work-Energy theorem, any change of energy of a system comes about by work being done on the system.

If the lever didn't do the same amount of work as you did on the lever, energy would be created or destroyed. This would violate a fundamental principle in physics: The Conservation of Energy.

Answer 2

A lever trades distance for force. From the definition of work, \[W = F*d\]So if we want to move a 10 N object 1 meter, we can set up a lever that requires 10 m of travel and 1 N of input force.