Context: Stellar evolution in close binary systems is strongly influenced by mass transfer from one star to the other when one component fills its zero-velocity surface or Roche Lobe. SS Lep is a fairly nearby close binary showing the Algol paradox and a shell spectrum, both indicative of (past) mass transfer. Aims: To study the process of mass transfer and its evolutionary consequences, we aim at a direct characterisation of the spatial dimensions of the different components of SS Lep with IR interferometry. Methods: We use VINCI/VLTI interferometric observations in the K band and photometric observations from the UV to the far-IR. The visibilities are interpreted with simple geometrical models and the Spectral Energy Distribution (SED) is decomposed into the three main components: A star, M star and dust shell/disk. Results: From the SED, we find that the main emitters in the K band are the M star and the circumstellar environment. Both are spatially resolved with the VINCI observations, showing the excess to be circumbinary and showing the M star to have a size equal to its Roche Lobe. Conclusions: We conclude that, for the first time, we have directly resolved a star filling its Roche Lobe. The resulting mass transfer is probably the cause of (1) the circumbinary dust disk of which we see the hot inner region spatially resolved in our observations, (2) the unusually high luminosity of the A star and (3) the shell spectrum seen in the UV and optical spectra.