The present work investigates heat conduction from lattice vibrations in a class of materials called half-Heuslers. The composition under investigation was XNiSn half-Heusler alloys where X=Ti, Zr or Hf. These materials have received a lot of attention for their favorable properties for hermoelectric applications. However, their lattice thermal conductivity is too high to be applicable as a thermoelectric material. Previous studies have shown that lattice thermal conductivity can be reduced by isoelectronic substitutions on the X-site or by reducing the grain size. The lattice thermal conductivity is calculated by using density functional theory and the phonon Boltzmann transport equation with the frozen phonon approach. Anharmonic three-phonon scattering was used to assess lattice thermal conductivity of pure TiNiSn, ZrNiSn and HfNiSn, the results had good accordance to experimental values. However, a slight overestimation was observed due to the fact that experimental samples exhibit microstructures which may affect the lattice thermal conductivity. The effect of alloying was then explored within the virtual crystal approximation, making it possible to screen all possible ternary substitutions in the composition Ti_x Hf_ y Zr_(1-x-y)NiSn. The lowest lattice thermal conductivity was found for the binary substitution where X=Ti and Hf, in the composition Ti_0.5Hf_0.5NiSn. Finally, a simple model for boundary scattering was used to quantify the effect of finite grain sizes on lattice thermal conductivity. Using values of the grain size obtained from experimental measurements as input when calculating lattice thermal conductivity showed very good accordance to experimental measurements of lattice thermal conductivity. This study demonstrated that modeling based on first principles can be used to quantify contributions from various scattering mechanisms and thus predict the thermal conductivity of given alloy compositions with a specific grain size.