Lattices in almost abelian Lie groups with locally conformal K\"ahler or symplectic structures

We study the existence of lattices in almost abelian Lie groups that admit left invariant locally conformal K"ahler or locally conformal symplectic structures in order to obtain compact solvmanifolds equipped with these geometric structures. In the former case, we show that such lattices exist only in dimension $4$, while in the latter case we provide examples of such Lie groups admitting lattices in any even dimension.