LZ Cen is a double-lined, near-contact but detached eclipsing binary consisting of two evolved early B stars (B0.5-B1). This paper presents the first photoelectric and spectroscopic analysis of the system, based on new light curves and spectroscopic data. uvby light curves were obtained with the Danish 50 cm telescope at ESO, La Silla (916 points in each colour). They were analysed with both the WINK model (Wood 1971, 1972) and the Wilson-Devinney (1971) program in its extended versions (Wilson 1979, 1993), adopting a circular orbit. The codes of both models were improved with modifications in the numerical solution procedure, and the Wilson-Devinney model has been implemented with the possibility of using tables of model atmosphere calculations, following the same philosophy as the WINK model. These modifications are documented here in some detail for future reference. The mass and luminosity ratios and rotations in the system are determined from a few photographic and CCD spectra. They show that the hotter component, eclipsed at primary eclipse, is also the smaller, less massive, and less luminous of the two stars. It was found difficult to obtain light curve solutions which were consistent with both the observed mass and luminosity ratios, but with the small number of spectra available, our best compromise solution yields M_A_=12.5Msun_, M_B_=13.5Msun_(+/-10%), R_A_=8.4Rsun_, and R_B_=9.1Rsun_(+/-3-4%). Both stars have temperatures close to 26500K and luminosities L_A_=3.1x10^4^Lsun_ and L_B_=3.6x10^4^Lsun_. With log g values as low as 3.66, the stars are obviously quite evolved and near the end of their life on the main sequence. We have explored the likely evolutionary state of LZ Cen in more detail by comparing its observed properties with the standard and overshooting models of Claret & Gimenez (1989, 1992). The analysis shows that both stars in LZ Cen have evolved to the very point of central hydrogen exhaustion or beyond if standard models are assumed, while LZ Cen is still well within the main-sequence band of the overshooting models, a rather more plausible scenario. In the latter case, models with Z=~0.01 fit the observed temperatures best for an age of some 12x10^6^yr, consistent with other recent results on young B stars.