As has been mentioned, “lifting” is not really the right term.
All bodies exert a “tidal effect” on each other. This effect has nothing to do with “tides” in the ocean. In fact the movement in the seas which will call tides are manifestations of the tidal effect of the moon upon the earth.
A tidal effect elongates the effected body in the direction of the body having the influence. This is apparent on solid matter to a lesser degree, but in the case of the earth the liquid seas form two “bulges” on opposite sides of the globe, in line with the moon. These form the “high tides” on the coasts and, because the earth is rotating they give the impression that they are moving from east to west, giving us two “high tides” per day. (The reason each high tide occurs about every twelve and a half hours and not twelve hours is because the moon is orbiting the earth every 28 days. Its apparent position – which dictates where the high tide occurs – thus changes daily.)