The use of computer simulation to predict the lattice thermal conductivity of materials has the potential to accelerate the discovery of new thermoelectric materials. However, the accurate prediction of this property from first principles, without input from experiment, is very computationally demanding, which limits the use of high-throughput strategies in thermoelectric materials design. We present here an accurate, fast, and non-empirical determination of the lattice thermal conductivities of a large family of semiconductors, with composition ABX2 (I-III-VI2), with A=Cu, Ag; B=Al, Ga, In, Tl; and X=S, Se, Te. We solve the Boltzmann transport equation with force constants derived from density functional theory calculations and machine-learning-based regression algorithms, reducing between one and two orders of magnitude the computational cost with respect to conventional approaches of the same accuracy. The results are in good agreement with available experimental data and allow us to rationalize the role of chemical composition, temperature and nanostructuring on the thermal conductivities across this important family of semiconductors.