CCD photometry of 809 Lundia obtained between September 2005 and January 2006 at Borowiec and Pic du Midi Observatories demonstrates that this object is a synchronous binary system with an orbital period of 15.418 ± 0.001 h. In this paper, we present the results of photometric observations of Lundia from two oppositions in 2005/2006 and 2007, as well as the first modelling of the system. For simplicity we assumed a fluid-like nature for each component with a modified Roche model and a triaxial ellipsoid shape in kinematic models. Our models provided similar results. Poles of the orbit in ecliptic coordinates are λ = 119 ± = 2°, β = 28 ± 4° (modified Roche) or λ = 120 ± = 5°, β = 18 ± 12° (kinematic). Triaxial ellipsoid shape solutions and a separation between components of 15.8 km are given after taking an equivalent diameter of 9.1 km from H = 11.8 mag and assuming an albedo of 0.4. The orbital period of the Lundia system obtained from modelling is the same as from the lightcurve analysis i.e., 15.418 ± 0.001 h. The bulk density of both components is 1.64 or 1.71 ± 0.01 g/cm3. The double system of Lundia probably originates from the fission process of a single body that could have been spun up by the YORP effect. The predicted lightcurves for future oppositions are also presented. © 2009 ESO.