Vertical and lateral heterostructures of van der Waals materials provide tremendous flexibility for band structure engineering. Since electronic bands are sensitively affected by defects, strain, and interlayer coupling, the edge and heterojunction of these two-dimensional (2D) systems may exhibit novel physical properties, which can be fully revealed only by spatially resolved probes. Here, we report the spatial mapping of photoconductivity in a monolayer-bilayer WSe2 lateral heterostructure under multiple excitation lasers. As the photon energy increases, the light-induced conductivity detected by microwave impedance microscopy first appears along the hetero-interface and bilayer edge, then along the monolayer edge, inside the bilayer area, and finally in the interior of the monolayer region. The sequential emergence of mobile carriers in different sections of the sample is consistent with the theoretical calculation of local energy gaps. Quantitative analysis of the microscopy and transport data also reveals the linear dependence of photoconductivity on the laser intensity and the influence of interlayer coupling on carrier recombination. Combining theoretical modeling, atomic scale imaging, mesoscale impedance microscopy, and device-level characterization, our work suggests an exciting perspective to control the intrinsic band-gap variation in 2D heterostructures down to the few-nanometer regime.