  Molybdenum based crystals such as Li$_2$MoO$_4$ and CaMoO$_4$ are emerging as
leading candidates for next generation experiments searching for neutrino-less
double beta decay with cryogenic calorimeters (CUPID, AMoRE). The exquisite
energy resolution and high radio-purity of these crystals come at the cost of a
potentially detrimental background source: the two neutrinos double beta decay
of $^{100}$Mo. Indeed, the fast half-life of this decay mode, combined with the
slow response of cryogenic calorimeters, would result in pile-up events in the
energy region of interest for neutrino-less double beta decay, reducing the
experimental sensitivity. This background can be suppressed using fast and high
sensitivity cryogenic light detectors, provided that the scintillation time
constant itself does not limit the time resolution. We developed a new
detection technique exploiting the high sensitivity, the fast time response and
the multiplexing capability of Kinetic Inductance Detectors. We applied the
proposed technique to a $2\times2\times2$ cm$^3$ Li$_2$MoO$_4$ crystal, which
was chosen as baseline option for CUPID. We measured simultaneously both the
phonon and scintillation signals with KIDs. We derived the scintillation time
constant of this compound at millikelvin temperatures obtaining $\tau_{scint} =
84.5\pm4.5\rm{(syst)}\pm1.0\rm{(stat)}$ $\mu$s, constant between 10 and 190 mK.
