Thermoluminescence (TL) properties of La2O3: Dy3+, Li+, and La2O3: Eu3+, Li+, exposed to 5.12 Gy of beta radiation, and recorded at different heating rates 0.5, 1, 2, 3, 4, and 5 °C s−1 (from Molefe et al., paper 2019), were analyzed and the trap parameters were determined in this study. These parameters include the order of kinetics b, the activation energy E (eV), the frequency factor S (s−1), or the pre-exponential factor S″ (s−1), and the initial concentration of trapped electrons no (cm−3). A new non-linear curve fitting technique, based on the general order kinetic equation and the outcomes of Hoogenstraaten’s Method, was established and applied on the TL glow peaks of La2O3: Dy3+, Li+. The fitting technique was evaluated by calculating the R-square and figure of merit (FOM) values. The results revealed that the FOM values are 0.997, which demonstrates an excellent convergence between experimental and fitted curves. A modified technique based on the three-points analysis method was exploited to deconvolute complex TL glow curves of La2O3: Eu3+, Li+, and in turn, to determine the trap parameters the method disclosed that each TL glow curve consists of four peaks. The trap parameters of the individual peaks were numerically determined. The fading, as a function of storage temperature and time, from the TL signals of the investigated materials was predicted and discussed based on the calculated trap parameters. The results support the value of the materials for employment in radiation dosimeter applications with a low fading fraction.