  We study locally conformal symplectic (LCS) structures of the second kind on
a Lie algebra. We show a method to build new examples of Lie algebras admitting
LCS structures of the second kind starting with a lower dimensional Lie algebra
endowed with a LCS structure and a suitable representation. Moreover, we
characterize all LCS Lie algebras obtained with our construction. Finally, we
study the existence of lattices in the associated simply connected Lie groups
in order to obtain compact examples of manifolds admitting this kind of
structure.
