A statistical analysis of random lasing events observed in dye-doped nematic-liquid-crystal films is reported. The occurrence of random laser action in such complex fluids is due to residual resonances in the multiple scattering of spontaneously emitted photons. The Shannon entropy and a local-Poisson test are used here in order to quantitatively characterize the chaotic behavior of laser spikes and gain further understanding of the mechanisms underlying the lasing effect in strongly scattering organized fluids arising by an unexpected interplay of localization and amplification.