Thermal conductivity plays a crucial role in many applications; use of single-crystal and textured polycrystalline materials in such applications necessitate understanding the anisotropy in thermal transport. Measurement of anisotropic lattice thermal conductivity is quite challenging. To address this need through computations, we build upon our previously developed isotropic model for kL and incorporate the directional (angular) dependence by using the elastic tensor obtained from ab initio calculations and the Christoffel equations for speed of sound. With the anisotropic speed of sound and intrinsic material properties as input parameters, we can predict the direction-dependent kL. We validate this new model by comparing with experimental data from the literature – predicted kL is within an average factor difference of 1.8 of experimental measurements, spanning 5 orders of magnitude in kL. To demonstrate the utility and computational-tractability of this model, we calculate kL of ~2200 layered materials that are expected to exhibit anisotropic thermal transport. We consider both van der Waals and ionic layered structures with binary and ternary chemistries and analyze the anisotropy in their kL. The large-scale study has revealed many layered structures with interesting anisotropy in kL.