The question Did DSCOVR travel “along the stable manifold of it's 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 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?