  Starting from a recently proposed framework for the evaluation of the
cosmological averages, we evaluate the higher-order moments for the
distribution of a given observable. Then, we explicitly discuss the case of the
Hubble-Lema\^itre diagram and evaluate its skewness at the leading order in the
cosmological perturbative expansion of the gravitational potential. In
particular, we focus on perturbations of the luminosity distance due to
gravitational lensing. Finally, we discuss our findings in view of recent
numerical relativistic simulations, confirming that the skewness in the
Hubble-Lema\^itre diagram primarily originates from the late-time matter
bispectrum, with other line-of-sight projection effects being sub-dominant.
