Open-aperture Z-scan measurements have been carried out to investigate the three-photon (3 PA) and four-photon absorption (4 PA) coefficients at 800 nm and 1030 nm wavelengths, respectively in congruent and stoichiometric lithium niobate (cLN, sLN) with different concentrations of Mg doping. The laser pulse duration at the two wavelengths were 40 and 190 fs. The peak intensity inside the crystals varied between approximately 110 and 550 GW/cm2. The 3 PA and 4 PA coefficients were evaluated using a theoretical model and the results suggest that their minima are at or around the Mg doping level corresponding to the threshold for suppressing photo-refraction for both cLN and sLN. This result can be attributed to the contribution of crystal defects to the 3 PA and 4 PA processes. Furthermore, the 4 PA at 1030 nm exhibited greater nonlinear absorption than the 3 PA at 800 nm under the same intensity level. Possible reasons for this unexpected behavior are discussed. Overall, comparing the 3 PA and 4 PA values of these crystals will enable for selection of the optimum composition of LN crystal for efficient THz generation and for other nonlinear optical processes requiring high pump intensities.