We discuss particle tracking simulations in a storage ring with Lithium lens inserts designed for the transverse phase space cooling of muons by the ionization cooling. In a hard-edged magnetic element model, we demonstrate the equilibrium normalized transverse emittance of 0.3 mm*rad which is necessary for a Higgs Factory, a low energy mu+mu- Collider. For the 6 dimensional phase space cooling of muons, a method of using bent Lithium lenses were discussed.