The magnetic and electronic properties of the double perovskite Lu2MnCoO6 are studied by combining the ab-initio calculations and Monte Carlo simulation (MCs) based on the Ising model. This compound is constituted of two magnetic cubic sublattices: one occupied by Mn4+ with spin (s = 3/2) and other occupied by Co2+ with spin (sigma = 3/2). By using ab-initio calculations we compute the exchange coupling between Mn-Co sublattices. We also investigate the phase transitions and the magnetic stability of this compound. The Curie temperature is determined as well as the critical exponents. We show that the Lu2MnCoO6 compound belongs to the 3D-Ising universality class. (C) 2017 Elsevier B.V. All rights reserved.