Context : Lithium abundances in open clusters are a very effective probe of mixing processes , and their study can help us to understand the large depletion of lithium that occurs in the Sun . Owing to its age and metallicity , the open cluster M67 is especially interesting on this respect . Many studies of lithium abundances in M67 have been performed , but a homogeneous global analysis of lithium in stars from subsolar masses and extending to the most massive members , has yet to be accomplished for a large sample based on high-quality spectra . Aims : We test our non-standard models , which were calibrated using the Sun with observational data . Methods : We collect literature data to analyze , for the first time in a homogeneous way , the non-local thermal equilibrium lithium abundances of all observed single stars in M67 more massive than \sim 0.9 \mathrm { M _ { \odot } } . Our grid of evolutionary models is computed assuming a non-standard mixing at metallicity { [ Fe / H ] } = 0.01 , using the Toulouse-Geneva evolution code . Our analysis starts from the entrance in the zero-age main-sequence . Results : Lithium in M67 is a tight function of mass for stars more massive than the Sun , apart from a few outliers . A plateau in lithium abundances is observed for turn-off stars . Both less massive ( M \leq 1.10 \mathrm { M _ { \odot } } ) and more massive ( M \geq 1.28 \mathrm { M _ { \odot } } ) stars are more depleted than those in the plateau . There is a significant scatter in lithium abundances for any given mass M \leq 1.1 \mathrm { M _ { \odot } } . Conclusions : 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 . More work is clearly needed to accurately reproduce 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 .