Where does the input energy come from? What type of energy is being transformed to lift the elevator in the first place? ?

energy to lift the elevator comes partially from counterweights, which is energy of gravitational potential energy, stored when the elevator moved down.

Remainder of the energy comes from electric motors, and the energy for that comes from the electric utility, power company, and their energy comes from various sources, depending on company and time of day.

Sorry, my answer is "Anonymous" as your post is Anonymous. There is no need for an Anonymous question in this category, Most 'Anonymous' posts are trolls, maybe yours is not, but the high likelihood is there. If you post as yourself, I would be glad to help you with any problem you have.
I spend a lot of time on each problem, I just want to make sure it's for a worthwhile cause.