Does the orbital period of halo/Lissajous orbits around L1/2 points increase, decrease or stay the same when increasing the (average) orbital radius?
A function period(radius,m1,m2) would be cool, although I guess for Lissajous orbits it would require additional parameters.
At some large radii the orbits would probably become unstable.
As the halo orbits grow out of plane, their orbital periods generally decrease. You can see a plot of the period (in days) of the L1 and L2 halo families at the Moon as a function of the closest approach distance from the Moon (rp) in Figure 2 of this paper: https://engineering.purdue.edu/people/kathleen.howell.1/Publications/Conferences/2017_AAS_DavPhiHow.pdf
In the Earth-Moon system, the range from around 2 weeks for nearly-planar halos to less than a week for the smallest NRHOs at L2.
The orbits actually get more stable as the families grow out of plane. The flatter halos are unstable.
