I'm trying to design a trajectory that takes a spacecraft from Sun-Earth L2 to a lunar flyby, to an Earth flyby and then to Mars (two flybys might be too complex, I might just do one). I've optimized a variety of interplanetary trajectories in GMAT with initial guesses generated from a simple software called Trajectory Optimization Tool, which uses patched conics to give the user dates for the arrival at the various planets in the trajectory (see image for an example of its inputs and outputs).
The problem is that it uses patched conics and can only do interplanetary trajectories (so no Earth-Moon trajectories and the like), meaning it can't be used for what I'm trying to do. So how do mission designers go about getting a "first glance" or low-fidelity analysis of the dates they should be looking for for such trajectories? What software does what the one on the image does, but with Lagrange points and Earth-centered trajectories?