If I press a button which lifts an object with a lever from point A upwards to point B and then back downwards to point A, no work has been done on the system that includes the object and lever. If I do it with my arm, still no work has been performed on the object but is it correct to say that I'm doing work on the external system that includes my muscles?
While we don't go back in time, the displacement is in the opposite direction which creates a net zero work done, correct? I'm still assuming this is with the lever, not the arm.
The concept that you're talking about is just a silly physics definition of "work" which we don't actually use in common language. What we normally mean by "work" is "expended energy".
To answer your question...no, no "work" has been done if they're back where they started.
In fact no net work has been done on the object, but the state of the system (you plus the object) will be changed. Often when energy is converted from one form to another, some is lost to entropy. When you raise the object, you are using a chemical reaction to convert energy stored in molecules into mechanical energy. However, when you lower the object back down the work you get back from the system is not being used to run the chemical processes in reverse (and probably can't be in all but the most idealized situations), but is being mostly wasted.
