You probably already found an answer by the time you posted this question, but I still give an answer in case it helps.
Using the orbital elements is the "right way" to do it. There are 6 of them, described in this Wikipedia article :
semi-major axis $a$
longitude of the ascending node $\Omega$
argument of ...
There isn't just one conversion, because the word "mean" can mean many
different things, depending on the context.
Specific formulae that may or may not help you include those in Kozai
1959, Brouwer 1959, and Walker 1967, and I'll have more to say
about them farther down, but the most important thing right now is to realize
there are lots of ...
It seems that they do. As @Diane noted in a comment, this paper (PDF freely available) discusses Lissajous orbits and approximation of their invariant manifolds: Europa Lander Trajectory Design Using Lissajous Staging Orbits
Lissajous orbits and approximation of their invariant manifolds are used to generate landing trajectories to the surface of ...