Although various hydrometallurgical and solvometallurgical efforts have been made to extract REEs from end-of-life (EoL) products and waste, a systematic and statistical analysis of the impacts of leaching parameters to optimize the leaching process using organic acids is necessary, but lacking in the literature. This study employed the response surface methodology to develop mathematical models for optimal leaching by levulinic acid (LevA) of REEs in two waste materials, namely red mud and spent fluorescent lamp phosphors. The established models exhibited excellent statistical properties, in terms of significance, fitting, prediction, and error distribution. For red mud, the optimal conditions of liquid-to-solid ratio (L/S; v/w) of 40, temperature of 70 °C, and duration of 60 h led to 100% leaching of REEs excluding Sc. At the same L/S and temperature, >98.7% of REEs were leached from fluorescent phosphors after 96 h. The SEM–EDS analysis of the waste materials revealed and confirmed morphological and compositional changes after leaching under the optimal conditions.