The LOPES experiment, a digital radio interferometer located at KIT (Karlsruhe Institute of Technology), obtained remarkable results for the detection of radio emission from extensive air showers at MHz frequencies. Features of the radio lateral distribution function (LDF) measured by LOPES are explored in this work for a precise reconstruction of two fundamental air shower parameters: the primary energy and the shower Xmax. The method presented here has been developed on (REAS3-)simulations, and is applied to LOPES measurements. Despite the high human-made noise at the LOPES site, it is possible to reconstruct both the energy and Xmax for individual events. On the one hand, the energy resolution is promising and comparable to the one of the co-located KASCADE-Grande experiment. On the other hand, Xmax values are reconstructed with the LOPES measurements with a resolution of 90 g/cm2 . A precision on Xmax better than 30 g/cm2 is predicted and achievable in a region with a lower human-made noise level.