A low energy transfer from the Earth to the Moon is proposed in the context of the 4-body Problem. We propose a new model by regarding the Sun-Earth-Moon-Spacecraft (S/C) 4-body system as the coupled system of the Sun-perturbed 3-body system and the Moon-perturbed 3-body system. In particular, we clarify the tube structures of invariant manifolds of the 4-body Problem by investigating the Lagrangian coherent structures of such a coupled 3-body system with perturbations. Lastly, we construct a low-energy transfer trajectory from the Earth to the Moon by patching two trajectories obtained from the perturbed systems at a Poincare section. We develop an optimal trajectory by minimizing the Delta-v at the Poincaré section.