Using density functional theory within the LSDA + U method, we investigate the effect of strain on the spin state and magnetic ordering in perovskite lanthanum cobaltite, LaCoO3. We show that, while strain-induced changes in lattice parameters are insufficient to stabilize a non-zero spin state, additional heteroepitaxial symmetry constraints -- in particular the suppression of octahedral rotations -- stabilize a ferromagnetic intermediate-spin state. By comparing with experimental data for the bulk material, we calculate an upper bound on the Hubbard U value, and describe the role that the on-site Coulomb interaction plays in determining the spin-state configuration.