In this study, we have explored the structural, electronic and thermal properties of La$_x$Sc$_{1−x}$N ternary alloys in rock-salt structure using the full-potential linearised augmented plane wave (FP-LAPW) method based on the density functional theory (DFT). To calculate the exchange-correlation energy and potential, we have used the Wu–Cohen generalised gradient approximation and the modified Becke–Johnson. We investigated the effect of composition on lattice parameters, bulk modulus and band gap. The variation of the calculated lattice constant with lanthanum composition is practically linear and shows a small deviation of the obtained results from Vegard’s law. Moreover, the effect of thermal macroscopic properties was also investigated employing the quasiharmonic Debye model, which takes into account the lattice vibrations. We have found a good accord between our results, the experimental data and previous theoretical results available in the literature for the binary compounds which can be a support for the ternary alloys in the future.