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The dynamics of solar-sail maneuvers are conceptually different from classical control maneuvers where one considers impulsive changes in the velocity of a spacecraft. Solar-sail orbits are continuous in both position and velocity in a varying vectorfield, opening the possibility of the existence of heteroclinic connections by means of artificially changing the vectorfield with a sail maneuver. This paper investigates solar-sail assisted maneuvers to obtain families of artificial heteroclinic connections between Lissajous libration point orbits. The study is based on a careful analysis of the geometry of the phase space of the linearized equations around the equilibrium points, the dynamical identification of the main parameters and the representation of the solutions in the action-angle variables. We identify the main dynamical properties of the connecting families presenting systematic new options for the mission analysis in the libration point regime using this technology, including a methodology to approach the classical problem of exclusion zone avoidance., D.X. thanks the support of the Chinese Scholarship Council. G.G. thanks the Catalan grant government for the grant 2017SGR-1374, and MINECO-FEDER for the grant MTM2016-80117-P. J.J.M. thanks MINECO-FEDER for the grant MTM2015-65715-P and the Catalan government for the grant 2017SGR-1049. The authors are grateful for the valuable suggestions of the reviewers.