A complete methodology for the transfer between two Lissajous orbits around the same collinear equilibrium point is developed making use of the geometry of the phase space around these points. The result of the study gives both strategies to change the amplitudes of the Lissajous orbit and simple procedures to avoid the exclusion zone in an optimal way. The presentation is centered on the linear problem which provides good initial guesses for orbits of small amplitude, likethe requirements for the mission FIRST/Planck of the European Space Agency (ESA), where part of the results of this paper were used for the mission design.