The integration of lenses with array antennas (referred to as dome arrays) in future communication systems offers numerous benefits, including improved radiation efficiency, adaptability in different use cases, and reduced energy consumption. This article elaborates upon using a novel two-dimensional ray-tracing technique for rapid and accurate numerical evaluation of the far-field radiation properties of three-dimensional multilayer dome arrays. Moreover, we also investigate how to account in our model for the effect of mutual coupling in dome arrays. The accuracy of the method is validated by comparing the simulated radiation patterns from the proposed ray-tracing model with results generated by widely used full-wave simulation tools like CST.