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 $2times2times2$ 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 $tau_{scint} = 84.5pm4.5rm{(syst)}pm1.0rm{(stat)}$ $mu$s, constant between 10 and 190 mK.
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