Putting an elevator (or more likely a sky hook) at a lunar Langrange point makes some sense, because the tether doesn't have to reach the entire distance if we allow for 0.2km/sec injection/drop-off speeds. That's important, because lunar elevator/hooks are much longer than earth based equivalents, even though their strength and taper ratios are much more achievable (e.g. polyethylene 4:1). You'd want to keep launched weight for the tether as low as possible.
A huge advantage is that a hook at the far lunar Lagrange 2 would be very close to escape velocity (e.g. asteroids or GEO).
A huge advantage is that a hook at the far lunar Lagrange 2 would be very close to escape velocity (e.g. asteroids or GEO).
http://hopsblog-hop.blogspot.com/2016/08/lunar-sky-hook.html
http://hopsblog-hop.blogspot.com/2015/05/eml2.html