If a satellite loses energy it starts to circle lower and finally hits the atmosphere. The moon is moving like an inch a year away from the earth even though it is losing energy pulling the oceans around.
No. The energy budget of the Moon is actually increasing. The Earth's spin is slowing down, and that energy gets transferred to the Moon.
Whatever else may be happening (like the losses you mention), this transfer from Earth's spin to Moon's orbital energy is the main process responsible for raising the Moon's orbit.