We report the structural and optical properties of Nd:YAB (NdxY1−x Al3(BO3)4)-nanoparticle-doped PDMS elastomer films for random lasing (RL) applications. Nanoparticles with Nd ratios of x = 0.2, 0.4, 0.6, 0.8, and 1.0 were prepared and then incorporated into the PDMS elastomer to control the optical gain density and scattering center content over a wide range. The morphology and thermal stability of the elastomer composites were studied. A systematic investigation of the lasing wavelength, threshold, and linewidth of the laser was carried out by tailoring the concentration and optical gain of the scattering centers. The minimum threshold and linewidth were found to be 0.13 mJ and 0.8 nm for x = 1 and 0.8. Furthermore, we demonstrated that the RL intensity was easily tuned by controlling the degree of mechanical stretching, with strain reaching up to 300%. A strong, repeatable lasing spectrum over ~ 50 cycles of applied strain was observed, which demonstrates the high reproducibility and robustness of the RL. In consideration for biomedical applications that require long-term RL stability, we studied the intensity fluctuation of the RL emission, and confirmed that it followed Lévy-like statistics. Our work highlights the importance of using rare-earth doped nanoparticles with polymers for RL applications.