The polarization of $Lambda$ hyperons from relativistic flow vorticity is studied in peripheral heavy ion reactions at FAIR and NICA energies, just above the threshold of the transition to the Quark-Gluon Plasma. Previous calculations at higher energies with larger initial angular momentum, predicted significant $Lambda$ polarization based on the classical vorticity term in the polarization, while relativistic modifications decreased the polarization and changed its structure in the momentum space. At the lower energies studied here, we see the same effect namely that the relativistic modifications decrease the polarization arising from the initial shear flow vorticity.