  Random coincidences of nuclear events can be one of the main background
sources in low-temperature calorimetric experiments looking for neutrinoless
double-beta decay, especially in those searches based on scintillating
bolometers embedding the promising double-beta candidate $^{100}$Mo, because of
the relatively short half-life of the two-neutrino double-beta decay of this
nucleus. We show in this work that randomly coinciding events of the
two-neutrino double decay of $^{100}$Mo in enriched Li$_2$$^{100}$MoO$_4$
detectors can be effectively discriminated by pulse-shape analysis in the light
channel if the scintillating bolometer is provided with a Neganov-Luke light
detector, which can improve the signal-to-noise ratio by a large factor,
assumed here at the level of $\sim 750$ on the basis of preliminary
experimental results obtained with these devices. The achieved pile-up
rejection efficiency results in a very low contribution, of the order of $\sim
6\times10^{-5}$ counts/(keV$\cdot$kg$\cdot$y), to the background counting rate
in the region of interest for a large volume ($\sim 90$ cm$^3$)
Li$_2$$^{100}$MoO$_4$ detector. This background level is very encouraging in
view of a possible use of the Li$_2$$^{100}$MoO$_4$ solution for a bolometric
tonne-scale next-generation experiment as that proposed in the CUPID project.
