Time lag distributions (black histograms) obtained by cross-correlating the simulated GBM and LAT light curves. Positive time lags correspond to the LAT signal lagging the GBM signal. The asymmetric Gaussian fit is reported as a blue solid line. The red areas correspond to the distributions of time lags obtained considering those fits that are significant at a 4σ level or higher, according to the χ² statistics (i.e., fits with χ²/ d.o.f. ≳3 are rejected). The asymmetric Gaussian fit for the red areas is reported as a blue dashed line.