Jerome Pearson, who left us January 2021, proposed a "Lunar Space Elevator"; duplicating work Yuri Artsutanov (m. 2019) had already done ~1960. The Spaceline, if I read this right, is a subset of the LSE. Pearson's scheme is best-known to readers of Arthur Clarke's Fountains of Paradise (1979).
These two physicists upon discovering they'd crossed streams agreed to meet in person, I hear, 2006. They accepted dual authorship: which was a mighty fine thing for Artsutanov to permit, and for Pearson to accept. Would that Russians and Americans got along so well today!
Anyway Pearson got with a few other doodz to sum-up his (part of the) scheme in a 2004 paper (pdf) and a Powerpoint presentation (pdf). It proposes more elevators from the L1 switching-station (which spaceline allows to make the main lunar hab) to the poles - starting with the south, where there's water.
The paper suggests an additional elevator through to TLL2 and... beyond. Nobody much seems to have calculated the length of this far tether toward, next-up, the ultra-high orbits and full STL2. Nor the tether's shape; I assume it bends. It might not need as much mass as the spaceline.
Also here are ribbon-climbers with some friction against the cable(s). They didn't consider a pulley-system. I might prefer pulley(s) over a long continuous cable which, as the 2004 paper notes, is vulnerable to meteors. Near the surface this must include dust kicked off from the low-grav lunar surface by high-energy activities there, which may even involve aluminum-dust rockets.
Pearson - per the paper - gets extra credit for understanding Jacobi's keyhole. Basically once you've paid your electric toll to get Lunar materiel to L1, the delta-V to get it to any other Earth or Lunar orbit - or even L2 - is zero. I mean, L1 wants a little oompf to push it off (hell, you can use spinlaunch here) and then reinsert it into your new orbit; but all that is up to you. L1 will take a hit to get stuff over the humps to L4 or L5 (or indeed STL4/5); such that people over there may just want Lunar rocks yeeted over there directly, or to grab meteor rubble.
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