This is the second paper in a series devoted to the study of massive binary systems in the Large Magellanic Cloud (LMC). We mainly aim to provide accurate data that constrains the mass-luminosity relation for the most massive stars but also to address the long lasting problem known as the "mass discrepancy." We present here our results for three binaries (LMC 169782, LMC 171520, and [P93] 921) harboring the earliest O-type components-ranging from O4 V to O6.5 V-among our sample of 17 systems. Our photometry provided accurate periods for the studied systems, allowing the spectroscopic observations to be performed at selected phases where the radial velocity separation between binary components is larger. Following the procedure outlined in our first paper of this series, after solving the radial velocity curves for orbital parameters, we used tomographic reconstruction to obtain the individual spectra of each star, from which we determined effective temperatures via a model atmosphere fitting with FASTWIND. This information, combined with the light-curve analysis that was performed with GENSYN, enabled the determination of absolute masses, radii, and bolometric luminosities that are compared with those predicted by modern stellar evolutionary models finding that they agree within the uncertainties. Nevertheless, the comparison seems to confirm the small differences found in the first paper of this series in the sense that the evolutionary masses are slightly larger than the Keplerian ones, with differences averaging ~10%, or alternatively, the stellar evolutionary models predict luminosities that are somewhat lower than observed. Still, the overall agreement between the current evolutionary models and the empirically determined stellar parameters is remarkable.