We present a nonequilibrium study of the relaxation process in spin crossover solids using numerical simulations of a recently introduced two-variable elastic Ising-like model. We analyze the structural lattice distortions accompanying the relaxation from the metastable high-spin to the ground low-spin state as a function of cooperativity. In the highly cooperative case, a sigmoidal relaxation behavior of the high-spin fraction ${n}_{\text{HS}}$ is described, and it occurs jointly with a structural phase separation process. The mean lattice spacing follows a similar sigmoidal trend, owing to the interplay between electronic and lattice variables in the Hamiltonian. Weakly cooperative systems are characterized by single exponential relaxations of the high-spin fraction, the corresponding structural transformation proceeds homogeneously with a progressive relaxation of the mean lattice spacing. Long relaxation tail effects are also observed. We highlight the development of lattice strain accompanying the spin transition, and show that structural phase rebuilding proceeds in the late stage of the relaxation by releasing residual strain. Under specific conditions, a temporal decoupling between the electronic and lattice variables is observed, which may have direct applications for interpreting time-resolved spectroscopic or diffraction experiments and for elucidating unusual structural behaviors, such as the development of superstructures, modulated structures, or transient phases.