Energy
No, raising the loads requires energy. That is supplied by a large orbital power station. There is not loss or gain of momentum that is not included in the calculations. There is even an acceleration on the cable from the Earths magnetic field that will have to be taken into account.
That is all taken care of in the overall totals.
Long term, the total energy up and down will balance. If not, the planet would either be slowed down or sped up. But, it might take a million years to be able to measure it.
by the way, the Moon is slowing down the Earth anyway. Earth is also speeding up the Moon too. Someday (in about 5 Billion Years) the Earth will fling the Moon off into space.
Meanwhile, the Sun is slowly changing the earths orbital speed too. (Geological change is rapid in comparison to how fast the Solar Orbit is changing.)
Space is complicated.
