But still lifting an object which could be heavy and will have to contain some kind of engine and fuel ie more weight and pull itself up a 1 to 4mm cable made out of carbon nanotubes, there is a traction issue especially as you'll have a ice frozen area. Unless it's like a Ski Lift system, if attached to and the tether rotates, some coming down and some coming up, but on that scale ?? You could power that earth side or both maybe solar from the station. Feasible yes, long shot ohhhh yes!!! 1 tiny strike by anything in orbit and and everything on the line comes crashing back to earth.
Carbon nanotubes are a good conductor so no fuel needed, just an electric motor. But yes, of course, material science needs to advance a bit to make this feasible.