  We study Jacobi-Lie Hamiltonian systems admitting Vessiot-Guldberg Lie
algebras of Hamiltonian vector fields related to Jacobi structures on real
low-dimensional Jacobi-Lie groups. Also, we find some examples of Jacobi-Lie
Hamiltonian systems on real two- and three- dimensional Jacobi-Lie groups.
Finally, we present Lie symmetries of Jacobi-Lie Hamiltonian systems on some
three-dimensional real Jacobi-Lie groups.
