This work presents the results from experiments performed on Lu2SiO5:Ce (LSO:Ce). It looks for potential correlations of light yield nonproportionality and other scintillation properties such as intrinsic energy resolution with thermoluminescence properties. The analyzed samples were chosen from various crystal batches having significantly different properties. Single crystal LSO:Ce samples were coupled to an XP2020Q photomultiplier and to large area avalanche photodiodes and measured as a function of gamma-ray energy between 14.7 and 1770 keV at room temperature and also near liquid nitrogen temperature. To explain the experimental results obtained from spectrometric methods, the properties of the samples were further studied using thermoluminescence techniques within the temperature range from 250 K to 600 K. The relationships between data obtained from these two types of experiments are reported.