We report a giant thermoelectric figure of merit $ZT$ (up to six at 1100 K) in $n$-doped lanthanum oxysulphate LaSO. Thermoelectric coefficients are computed from ab initio bands within Bloch-Boltzmann theory in an energy-, chemical potential-, and temperature-dependent relaxation time approximation. The lattice thermal conductivity is estimated from a model employing the ab initio phonon and Gr\"uneisen-parameter spectrum. The main source of the large $ZT$ is the significant power factor which correlates with a large band complexity factor. We also suggest a possible $n$-type dopant for the material based on ab initio calculations.