Aims: We determine the physical properties (spin state and shape) of asteroid (21) Lutetia, target of the International Rosetta Mission of the European Space Agency, to help in preparing for observations during the flyby on 2010 July 10 by predicting the orientation of Lutetia as seen from Rosetta. Methods: We use our novel KOALA inversion algorithm to determine the physical properties of asteroids from a combination of optical lightcurves, disk-resolved images, and stellar occultations, although the last are not available for (21) Lutetia. Results: We find the spin axis of (21) Lutetia to lie within 5° of (λ = 52°, β = -6°) in the Ecliptic J2000 reference frame (equatorial α = 52°, δ = +12°), and determine an improved sidereal period of 8.168 270±0.000 001 h. This pole solution implies that the southern hemisphere of Lutetia will be in "seasonal" shadow at the time of the flyby. The apparent cross-section of Lutetia is triangular when seen "pole-on" and more rectangular "equator-on". The best-fit model suggests there are several concavities. The largest of these is close to the north pole and may be associated with strong impacts. © ESO 2010.