Context. A high fraction of massive stars are found to be binaries but only a few of them are reported as photometrically variable. By studying the populations of double-lined spectroscopic binaries in the 30 Doradus region, we found a subset of them that have photometry from the OGLE project and that display variations in their light curves related to orbital motions. Aims. The goal of this study is to determine the dynamical masses and radii of the 26 binary components in order to investigate the mass-discrepancy problem and to provide an empirical mass-luminosity relation for the Large Magellanic Cloud (LMC). Methods. We use the PHOEBE programme to perform a systematic analysis of the OGLE V and I light curves obtained for 13 binary systems in the 30 Doradus region. We adopt the effective temperatures, and orbital parameters derived previously to obtain the inclinations of the systems and the parameters of the individual components. Results. Three systems display eclipses in their light curves, while the others only display ellipsoidal variations. We classify two systems as over-contact, five as semi-detached, and four as detached. The two remaining systems have uncertain configurations due to large uncertainties on their inclinations. The fact that systems display ellipsoidal variations has a significant impact on the inclination errors. From the dynamical masses, luminosities, and radii, we provide LMC-based empirical mass-luminosity and mass-radius relations, and we compare them to other relations given for the Galaxy, the LMC, and the Small Magellanic Cloud. These relations differ for different mass ranges, but do not seem to depend on the metallicity regimes. We also compare the dynamical, spectroscopic, and evolutionary masses of the stars in our sample. While the dynamical and spectroscopic masses agree with each other, the evolutionary masses are systematically higher, at least for stars in semi-detached systems. This suggests that the mass discrepancy can be partly explained by past or ongoing interactions between the stars.