We report on nanoscopic exploration of the luminescence from individual InP quantum dots (QDs) by means of highly spatially resolved cathodoluminescence (CL) spectroscopy directly performed in a scanning transmission electron microscope (STEM). A 7-fold layer stack with highdensity InP quantum dots is embedded as an active medium membrane in an external-cavity surface-emitting laser. We characterize the vertical transfer of carriers within the periodic separate confinement heterostructure and determine the capture efficiency of carriers from the cladding layer into the quantum dot layers. Benefiting from the nanoscale resolution of our STEM-CL, we perform single-dot spectroscopy on single isolated QDs in the STEM lamella resolving the details of the excitonic structure of individual quantum dots. Executing highly spatially resolved spectrum line scans within the QD layers, we directly visualize the lateral transport, i.e., the efficient lateral capture of carriers into an individual QD. We observe a characteristic change of the spectral fingerprint during this line scan, while the electron beam is approaching and subsequently receding from the quantum dot position. This directly correlates to the increase and decrease of the numbers of excess carriers reaching the dot, i.e., altering the quantum dot population. The characteristic shift of emission energies visualize the renormalization of the ground-state energy of the single dot, and the intensity ratio of the excitonic recombinations verifies this change of the occupation and the state-filling.