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In order to answer to some specific unsolved questions regarding ancient Roman frescoes from Villa della Piscina, already examined by other spectroscopic techniques, LIBS stratigraphic measurements were performed on the most representative sample fragments. We found that taking into account just the line intensities or applying a single normalization approach based on ratio of the element's analytical line and a selected transition from a main sample constituent, here of Ca, might produce misleading results of depth profiling by LIBS. During the laser induced ablation, parameters of the detected plasma might change both due to the crater development and different overlaid matrix materials, as in case of heterogeneous painted samples, possibly realized with different techniques. We performed the theoretical simulations to select the pair of Cu I and Ca I lines less sensitive to variations of the plasma temperature in presence of local thermal equilibrium (LTE). However, when using not gated detectors as here, the experimental results showed that only a partial LTE holds. For this reason, the choice of the optimum normalization line must take into account also the energy gap between the excited levels of the species, which energies affect the emission lifetime and consequently, the intensity captured by not gated detectors. In following, to the each element's analytical line a specific Ca I line was attributed for deducing the relative element distribution in sample. Following this approach and by detecting simultaneously up to 20 elements per laser pulse, it was possible to distinguish clearly by LIBS also thin overpainted layers of similar colour, and to recognize the painting technique used. Through detection of trace and light elements and studies of their correlations with other elements during ablation of on painted layer, in some cases it was possible also to establish the geographical provenance of the material used.