Random lasers are highly configurable light sources that are promising for imaging and photonic integration. In this study, random lasing action was generated by optically pumping N-(4-methoxybenzylidene)-4-butylaniline (MBBA) liquid crystals infiltrated with gold nanoparticles and a laser dye (pyrromethene 597 (PM597)). By varying the pump energy near a lasing threshold, we show that it is possible to control intensity correlations between random lasing modes. The correlations in the system were phenomenologically characterized using the Levy statistics of the emission spectrum survival function. We also find that correlations and persistence of lasing action are correlated. These results demonstrate the possibility to dynamically control a key physical feature of random lasers, which may find applications in biomedical settings and network communications.