Lateral heterostructures of two-dimensional (2D) transition metal dichalcogenides offer promise as platforms for a wide variety of applications from exotic physics to environmental control. Further development and study of these heterostructures require characterization methods that assess the quality of the heterostructures. Here, we extend current characterization strategies to create photoluminescence (PL), Raman, reflection contrast, and second harmonic generation (SHG) maps of individual monolayer core-shell WS2-MoS2 lateral heterostructures that were synthesized via water vapor assisted chemical vapor transport. Together, these methods provide the correlations required to resolve the effects of excitons, trions, lattice defects, strain, and alloying. The comparisons show substantial differences, especially in the regions near and at the narrow heterointerface. Comparisons between the different spectral maps show the importance of metal alloying for understanding the electronic and spatial structures of heterostructures. The results are compared to previous work on similar lateral heterostructures created by different methods.