The copper-doped lithium tetraborate Li2B4O7 (LBO) is one of the promising materials for the thermoluminescent dosimetry since it possesses the best tissue-equivalence among known non-organic materials used in the dosimetry. In addition, this material has high radiation resistance, a linear dose dependence, a wide range of operating doses and an insignificant dependence of a dose on the ionizing radiation energy. However, the results of the studies on the local attachment level parameters, which define the dosimetric properties of Li2B4O7:Cu, obtained by various authors differ considerably. To some extent, this descrepancies are due to the different purity of the initial materials and the technology of luminophor preparation, the methods of measuring the thermostimulated luminescence (TSL) and determining the parameters from the temperature luminescence glow curves (TLGC). In the present paper, the studies of the integral TSL in the polycristalline and monocrystalline LBO have been carried out at different heating rates. By means of a partial luminescence overall light collection method the energy positions of the local attachment levels have been determined, while the TLGC computer simulation technique has allowed the corresponding frequency factors to be found.