Rare-earth monopnictides have attracted much attention due to their unusual electronic and topological properties for potential device applications. Here, we study rock-salt structured lanthanum monopnictides LaX (X = P, As) by density functional theory (DFT) simulations. We show systematically that a meta-GGA functional combined with scissor correction can efficiently and accurately compute the electronic structures on a fine DFT k-grid, which is necessary for converging thermoelectric calculations. We also show that strain engineering can effectively improve the thermoelectric performance. Under the optimal conditions of 2% isotropic tensile strain and carrier concentration n = 3 × 1020 cm-3, LaP at a temperature of 1200 K can achieve a figure of merit ZT value >2, which is enhanced by 90% compared to the unstrained value. With carrier doping and strain engineering, lanthanum monopnictides thereby could be promising high-temperature thermoelectric materials.