X-ray absorption near-edge spectra (XANES) of Ta-L₂ and L₃ edges in LiTaO₃ (LTO) crystals are measured by measuring amplitude and phase of thermal waves generated within the LTO crystal, using pyroelectric property of LTO. Thus, LTO crystal is used both as a sample as well as sensor material. XANES of Ta-L edges in LTO are also measured by fluorescence. XANES spectra from fluorescence and first-principles simulations agree excellently well. The onset of the pre-edge region of XANES, measured by both techniques, extends below the edge by about 50 eV. This pre-edge onset of absorption is explained in terms of the core-hole lifetime effect on near-edge absorption using density functional theory. However, detailed nature of XANES peaks near Ta-L₃ and Ta-L₂ absorption edges, measured by thermal waves and fluorescence, differ. Possible origins of these differences are discussed.