This article explores the statistics of spectral features, particularly shot-to-shot intensity fluctuations, in a potassium sodium niobate-dye colloidal system used as a random lasing platform. Correlations between spectral intensity fluctuations were analyzed in the random laser medium, where scatterer displacement considerably varies between consecutive shots. The report investigates the underlying physical process like replica symmetry breaking by studying the spectral intensity fluctuations in the emission intensity. Pearson correlation coefficients were calculated to better understand these correlations, and correlation plots (heatmaps) were generated. A single parameter () derived from an -stable Lévy fit characterized the intensity distributions in all regimes. The spectral position and spacing of the spikes were examined to gain better insights into the random lasing spectra. Additionally, the Parisi overlap parameter and the exponent are calculated, establishing the two parameters as an indicator of threshold energy. Finally, the paper explored photonic phases and fluctuation regimes, highlighting their importance in the broad range of applications for random lasers.