The cycling stations will follow highly elliptical orbits with a perigee just a few thousand kilometers from Earth and an apogee at about 470,000 km. (292,000 miles) from Earth.  The stations will follow 13.66 day orbits (one-half the lunar orbital period) and arrive near the Moon once a month on every other orbit.  It will take about a week to reach the vicinity of the Moon.  Travelers will board the taxi and ride over to a station at L2, then descend to the lunar surface in landers which I dub "Moon Shuttles."

The actual complexities of the cycling stations'  orbits will require computer modeling.  We will be able to determine the position of the stations and the perturbations of their orbits by the Moon's gravity and even the slight effects of the solar wind and other planets of the solar system on the cyclers' orbits. We will know how much rocket power and fuel, probably Al and LUNOX, will be needed to adjust the stations' orbits.  We will also use solar electric propulsion with ample lunar magnesium for reaction mass to adjust orbits with great efficienty.  Solar sails or magnetic sails could also be used to make course corrections.  It might even be possible to build huge microwave beaming stations on the Moon and Earth to apply pressure to the solar sails and adjust the cyclers' orbits to compensate for the effects of perturbation without using any propellant at all.

ABOVE) The effects of the Moon's gravity on the cycler will tend to cancel out, thereby reducing the perturbations to a point that can be managed with Al+LUNOX and SEP thrusters on the station.

BELOW: Lots of cyclers=lots of monthly opportunities to fly to the Moon.  Numerous LEEO taxiports=more chances to rendezvous with cyclers

A Moon Shuttle by Peter Kokh

Lagrange points are not really points but regions in space.  We will not need one big spaceport station at a precise gravitational stability point in space.  We will build numerous stations in halo orbit around Lagrange "points" that use solar electric ion drives with lunar magnesium vapors for reaction mass, mag-sails and solar sails to stay on station. Halo orbits are possible at the three co-linear Lagrange points- L1, L2 and L3.  Earth-Moon L1, L2 and L3 are not as stable as L4 or L5, but it will take only tens of meters per second per year to stay on station, so there is no danger here as there is no danger of orbital decay from GEO.  It will probably take more fuel for reboost of stations in LEO where atmospheric drag does exist.