Lithium abundances in open clusters are a very effective probe of mixing processes, and their study can help to understand the large depletion of lithium in the Sun. Due to its age and metallicity, the open cluster M67 is especially interesting on this regard. Many studies on lithium abundances in M67 have already been performed, but a homogeneous global analysis of lithium in stars from subsolar up to the most massive members, was never accomplished for a large sample based on high-quality spectra. We tested our non-standard models, which were calibrated using the Sun with observational data. We collected literature data to follow, for the first time in a homogeneous way, NLTE lithium abundances of all observed single stars in M67 more massive than about 0.9 solar masses. Our grid of evolutionary models were computed with non-standard mixing at metallicity [Fe/H] = 0.01, using the Toulouse-Geneva evolution code. The analysis is started from the entrance in the ZAMS. Lithium in M67 is a tight function of mass for stars more massive than the Sun, apart of a few outliers. A plateau in lithium abundances is observed for turn-off stars. Both less massive and more massive stars are more depleted than those in the plateau. There is a significant scatter in lithium abundances for any given mass lower than M <= 1.1 solar masses. Our models qualitatively reproduce most of the features described above, although the predicted depletion of lithium is 0.45 dex smaller than observed for masses in the plateau region, i.e. between 1.1 and 1.28 solar masses. Clearly, more work is needed to throughly match the observations. Despite hints that chromospheric activity and rotation play a role in lithium depletion, no firm conclusion can be drawn with the presently available data.

14 pages, 4 figures, accepted by A&A