This chapter describes the application of Pontryagin’s maximum principle to the optimization of trajectories that escape from Earth’s sphere of influence, departing from the Earth–Moon L2 Lagrangian point. The dynamic model considers Sun, Earth, and Moon gravity as the main forces acting on the spacecraft; solar radiation pressure is also introduced. Electric propulsion is used by the spacecraft to exploit the unstable and chaotic dynamics at the Lagrangian point and move toward an unstable manifold and achieve escape. Sun’s perturbation is properly exploited to increase the spacecraft energy and drive it toward the escape. Specific techniques and improvements to the method are introduced to improve convergence of the indirect optimization approach and tackle the bang–bang nature of the thrust profile. Escapes trajectories may in fact have single-burn or two-burn solutions depending on the trajectory deflection that is needed to move the spacecraft toward regions where a favorable solar perturbation is exploited.