Moon Tether vs. Hareno-dynamic Landing
An earthwards tether from the Moon towards the Earth, reaching "beneath" the L1 point, is superficially plausible. At some radius, the angular velocity at the apogee of a loop-launched elliptical orbit will match the angular velocity of the Moon. A vehicle could latch on at that point, and climb the tether towards L1, then lower itself down to the lunar surface.
Without getting into details of barycenters and lunar gravitation, the apogee that does this is about 137,000 kilometers above Earth, still 245,000 kilometers from the lunar surface. 16 days of climber time at 100 m/s. That is a LONG road trip, almost 7 times as far as an Earth to Geostationary space elevator.
The "gravity" at attachment is 2 milligees earthward, decreasing to 0 milligees at L1, then increasing to 160 milligees at lunar "landing"
For comparison, consider the "differently crazy" lunar slide landing scheme proposed by Krafft Ehricke in 1976, and described in Acta Astronautica in 1983. Ehricke proposes using lunar dust to slow a vehicle down relative to the Moon. Ehricke calls the interaction with sand and dust "hareno-dynamics" ("hareno" is Latin for "of sand", and describes something like landing in surface dust with a bulldozer.
A vehicle in a high "lunar intercepting orbit" will have an Earth-relative apogee velocity of 185 m/s, slower than the Moon's Earth-relative orbital velocity of 1020 m/s. At some distance away, the vehicle will approach the Moon at 835 m/s. As it falls into the Moon's gravity well, it will pick up "escape" energy. Precisely aimed, it will skim the Moon's surface at 2520 m/s. That is faster than a 1680 m/s circular orbit, so after closest approach, the vehicle will ascend at 2 m/s².
Ehricke's idea is that the vehicle can "bulldozer" it's way over the lunar surface, hopefully not banging into anything big enough to rip holes in the blade. However, we can be more clever than that (perhaps ... Ehricke was very clever). We will replace some of Ehricke's clever with "brute force" precision, and presume established infrastructure on the Moon to aid incoming vehicles.
Instead, presume a 250 kilometer line of "dust mortars", launching packages of lunar dust into the path of the vehicle heat shield, acting like air does against aerodynamic heat shields on Earth reentry vehicles. Some of the material will miss, some will be deflected away from the flight path at a small angle, some will bounce off the vehicle nosecone (which may accumulate a "boundary layer" of hot fused dust and dust vapor). Presume 30 m/s² deceleration.
In the extreme best case, well placed dust can slow the vehicle to a stop, perhaps even provide some lift for a smooth and precise landing. Alternately, puffs of dust plus vehicle flight control surfaces can line up the vehicle for a precision landing on a launch-loop-like rail.
Lofting perhaps 10 times the vehicle's mass in lunar dust packages, up to perhaps 8 kilometers altitude in 1.6 m/s lunar gravity, would require 160 m/s of dust package launch velocity, perhaps 130 kJ per kilogram of vehicle mass, while helping it shed 3.2 megajoules per kilogram of vehicle kinetic energy. Compared to the rocket energy and fuel required for self-contained slowdown and descent, this may offer better than 50x energy and launch mass advantages compared to a rocket landing, and significant advantages compared to a long and slow space elevator from Earth-Moon L1. The energy can be collected and stored on the Moon instead of carrying it on the vehicle.
A good application is one-way delivery of material and machines to an isolated high-risk experimental biolab, this process cannot be used in reverse, allowing dangerous materials to leave the Moon. While some of the "hareno-entry dust" may end up in lunar orbit, and a tiny fraction escape the Moon into high Earth orbit, the delta V to solar orbit is less than the delta V to the Earth's surface. There will be many astrodynamic isolation barriers between lunar experiments and Earth contamination.
Practically speaking, a launch from Earth to the Moon cannot be "rocket free"; the Earth's equator tilts 23 degrees, and the Moon's orbit tilts 5 degrees, and precesses. Frequent launch windows (perhaps once per day) will require plane-changing thrust.
For time-insensitive lunar cargo (and most of the mass for a base will be cargo), this can be done by launching into a VERY high orbit, making a relatively small velocity change at apogee into the lunar orbital plane, then arriving at the Moon "hot".
A direct lunar transfer orbit from the loop to a near-lunar apogee of 384400 kilometers has a perigee an apogee velocity of