"My head hurts!"

For a space elevator you need to get to Geostationary orbit; on the Moon "Geostationary orbit" is Earth/Moon L-1 & 2 (or L4/5 which even further away). I believe that L-2 is further away from the moon than L-1. L-1 is about double the distance is comparison to distance from Earth to GEO. BUT the biggest problem with Space elevators in general is having material which will lift it's own weight over some distance- e.g.with Earth's gravity, you could have material which lift it own weight which was 10 miles long, since the Moon has 1/6 the gravity, this same material could instead be 60 miles long. So roughly for Lunar elevator, you need this elevator to be twice the length, but material would be effectively be 6 times stronger.
Now, with a Earth Elevator you also need an anchor- roughly, you get this by extending the elevator beyond GEO. Btw, I think the key to making a Earth elevator would be to have a massive object in GEO (a good size asteroid) and why this would be key is based on idea of the relatively cheap cost of getting a massive object to GEO and not needing to process on this mass.
Now, making a anchor at L-points for a Moon elevator could be a problem. Another problem would be the changing graviational forces- Moon is getting closer to Sun and distance to Earth changes and this significant because the Moon is a "relatively" weaker gravity- at L-1 or 2 the Moon isn't the dominate gravity- rather it's a Earth orbit affected by the Moon's gravity. Btw, I'm not saying these problems can't be easily solve [I haven't given them much thought- I don't think Lunar elevator is a very good solution, compared to others- like mass drivers or tethers].