Traditional half-Heusler thermoelectric materials, identified as 18-electron compounds, are characterized by the high power factor and the high lattice thermal conductivity. Interestingly, the emerging 19-electron half-Heusler compounds were also found to be promising thermoelectric materials, but with a 5-10 times lower lattice thermal conductivity. Since the two kinds of compounds have similar chemical and physical structures, such as TiCoSb and VCoSb, the large difference in lattice thermal conductivity is a puzzling question. Here, we present a theoretical study to clarify the lattice thermal transport in half-Heusler thermoelectric materials. Based on electronic band structure analysis, we show that the two transition-metal elements in half-Heusler compounds form the strong and direct d-d interaction that is responsible for the high lattice thermal conductivity of 18-electron compounds. In 19-electron half-Heusler compounds, however, the extra valence electron enters the d-d antibonding states, which significantly weakens the atomic bond strength, leading to a large decrease in the cohesive energy. The resulting softened acoustic phonons enhance the phonon-phonon scattering, and thus reduce the lattice thermal conductivity significantly. By constructing an artificial 18-e compound V0.5Sc0.5CoSb, it is proved that the one less electron relative to VCoSb increases the lattice thermal conductivity significantly.