Cryptic statement from my textbook

dEdt

This paragraph comes right after the authors derived the Hamiltonian of a rotating system, [itex]H=H_{\omega=0}-\omega l_z[/itex]:

"The noninertial effects of rotation would lead to a considerably more complicated form using Lagrangian instead of Hamiltonian dynamics. The simplicity of the Hamiltonian is not an accident, nor is it accidental that the dynamical quantity [itex]l_z[/itex] appears in it."

Unfortunately, the authors don't explain why rotation is more easily handled with Hamiltonians than with Lagrangians, nor why angular momentum appears in the equations. Can anyone help elucidate what they mean?