By Poissonization of Jacobi structures on real three-dimensional Lie groups G and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian systems on G ⊗ R.

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.