The question Did DSCOVR travel “along the stable manifold of its future SE L1 Halo orbit” to get there? is specific to DSCOVR's trajectory from Earth to its primarily heliocentric orbit near Sun-Earth L1, which is a Lissajous oribit.
Here I would just like to ask the general question: Do non-halo1 Lissajous orbits have stable/unstable manifolds? For those specific orbits where the horizontal and vertical periods are rational fractions (e.g. 3/2, 5/4) would the manifold just be a "cylinder-like" extension of the closed, periodic orbit? For example, if the ratio were 2:1 would it look like a figure-eight just extruded and stretched into the 3rd dimension?
1Halo orbits are a subset of Lissajous orbits where the oscillations in the plane of the two massive bodies (e.g. Earth's orbit around the Sun) and the oscillations out of plane (perpendicular to Earth's orbit) are the same, so that in the CR3BP approximation the orbit is perfectly closed and repeating. Lissajous orbits have that constraint relaxed, so the periods could be different by a tiny amount up to tens of percent or even more.