We compute the isospin-asymmetry dependence of microscopic optical model potentials from realistic chiral two- and three-body interactions over a range of resolution scales $Lambda simeq 400-500$,MeV. We show that at moderate projectile energies, $E_{rm inv} = 110 - 200$,MeV, the real isovector part of the optical potential changes sign, a phenomenon referred to as isospin inversion. We also extract the strength and energy dependence of the imaginary isovector optical potential and find no evidence for an analogous phenomenon over the range of energies, $E leq 200$,MeV, considered in the present work. Finally, we compute for the first time the leading corrections to the Lane parametrization for the isospin-asymmetry dependence of the optical potential and observe an enhanced importance at low scattering energies.