  Aims. We present a spectroscopic analysis of a sample of evolved stars in M67
(turn-off, subgiant and giant stars) in order to bring observational
constraints to evolutionary models taking into account non-standard transport
processes. Methods. We determined the stellar parameters (Teff, log g, [Fe/H]),
microturbulent and rotational velocities and, Lithium abundances (ALi) for 27
evolved stars of M67 with the spectral synthesis method based on MARCS model
atmospheres. We also computed non-standard stellar evolution models, taking
into account atomic diffusion and rotation-induced transport of angular
momentum and chemicals that were compared with this set of homogeneous data.
Results. The lithium abundances that we derive for the 27 stars in our sample
follow a clear evolutionary pattern ranging from the turn-off to the Red Giant
Branch. Our abundance determination confirms the well known decrease of lithium
content for evolved stars. For the first time, we provide a consistent
interpretation of both the surface rotation velocity and of the lithium
abundance patterns observed in an homogeneous sample of TO and evolved stars of
M67. We show that the lithium evolution is determined by the evolution of the
angular momentum through rotation-induced mixing in low-mass stars, in
particular for those with initial masses larger than 1.30 M_\odot at solar
metallicity.
