We present an investigation of defects acting as electron traps in ${\text{Lu}}_{2}{\text{SiO}}_{5}$ (LSO) and ${\text{Lu}}_{x}{\text{Y}}_{2\ensuremath{-}x}{\text{SiO}}_{5}$ (LYSO) performed by wavelength-resolved thermally stimulated luminescence (TSL) measurements from 20 to $400\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$ after room-temperature (RT) x-ray irradiation. Single crystals doped with several rare-earth ions such as Ce, Tb, Tm, and Sm were considered. A comparison between TSL and RT radio-luminescence (RL) emission spectra is also presented. The glow curves for both LSO and LYSO are similar, showing a series of TSL peaks at 78, 135, 181, and $236\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$. In addition, a further peak at about $300\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$ is observed only in LYSO. Our results confirm the role of oxygen vacancies as electron traps in the material; the presence of several glow peaks with a unique trap depth $(0.99\text{ }\text{eV}\ifmmode\pm\else\textpm\fi{}0.07\text{ }\text{eV})$ for the 78, 135, 181, and $236\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$ peaks is explained by suggesting that electrons stored in oxygen vacancies recombine through a thermally assisted tunneling mechanism with holes localized at ${\text{Ce}}^{3+}$ or ${\text{Tb}}^{3+}$ centers residing on Lu sites at different crystallographic distances from the traps. This model is supported by the very good correlation among O-Lu distances in the monoclinic $C2/c$ structure of LSO and LYSO and the frequency factors of the traps containing the transmission coefficients of the potential barriers between traps and centers, evaluated in the framework of the thermally assisted tunneling process. Tm and Sm ions do not act as TSL recombination centers possibly due to their tendency to trap electrons during irradiation with ionizing radiation.