Spin-crossover (SCO) solids have been studied for several years due to their fascinating physical properties and their potential applications as optical switches and reversible high-density memories for information storage. Through this article, we will examine in details the effects of substrate's lattice parameters, on a deformable spin crossover membrane, simulated using an electro-elastic model taking into account the volume change at the transition. The molecules of the membrane can be either in the low spin state (LS) or the high spin state (HS), while those of the substrate are electronically neutral. Magnetic properties of the SCO membrane and the pressure distribution as a function of the lattice parameter of the substrate have been investigated. We demonstrated that the thermally induced first-order spin transition is significantly affected by the structural properties of the substrate, where a rise in the lattice parameter of the latter lowers the transition temperature and reduces the width of the thermal hysteresis loop. The investigations on the spatiotemporal aspects of the spin transition in the membrane demonstrates that the nucleation and growth processes are sensitive to the structural properties of the elastic misfit between the substrate and the SCO membrane.