We present a study of the lithium abundances of a sample of evolved components of Chromospherically Active Binary Systems. We show that a significant part of them have lithium excesses, independently of their mass and evolutionary stage. Therefore, it can be concluded that Li abundance does not depend on age for giant components of CABS. These overabundances appear to be closely related to the stellar rotation, and we interpret them as a consequence of the transfer of angular momentum from the orbit to the rotation as the stars evolve in and off the Main Sequence, in a similar way as it happens in the dwarf components of the same systems and in the Tidally Locked Binaries belonging to the Hyades and M67. Based on observations collected with the 2.2,m telescope of the German-Spanish Observatorio de Calar Alto (Almeria, Spain), and with the 2.56,m Nordic Optical Telescope in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof\'i sica de Canarias (La Palma, Spain)