The moon doesn't have enough rotation for a fixed skyhook (space elevator) anyway.
You're just fairly restricted in where you can put it- you can only put one near the sub-Earth and anti-Earth points, such that the cable passes through the L1 or L2 Lagrange points, rather than anywhere along the equator. The cable would have to much, much longer than for a space elevator on Earth, but the Moon's lower gravity actually makes the engineering challenges Not As Bad- i.e., we could build a lunar space elevator with current materials.