  Measurements of lithium (Li) abundances in open clusters provide a unique
tool for following the evolution of this element with age, metallicity, and
stellar mass. Using FLAMES/Giraffe on the VLT, we obtained spectra of 157
candidate members of the old, metal-poor cluster Berkeley 32, to determine
membership and to study the Li behavior of confirmed members. Radial velocities
were measured, allowing us to derive both the cluster velocity and membership
information for the sample stars. The Li abundances were obtained from the
equivalent width of the Li I 670.8 nm feature, using curves of growth.We
obtained an average radial velocity of 105.2 +/- 0.86 km/s; 53 % of the stars
are confirmed as members.The Li - effective temperature distribution of
unevolved members matches the upper envelope of M 67, as well as that of the
slightly older and more metal-rich NGC 188.No major dispersion in Li is
detected. When considering the Li distribution as a function of mass, however,
Be 32 members with solar-like temperature are less massive and less Li-depleted
than their counterparts in the other clusters. The mean Li of stars in the
temperature interval 5750 < Teff < 6050 K is log n(Li)=2.47 +/- 0.16, less than
a factor of two below the average Li of the 600 Myr old Hyades, and slightly
above the average of intermediate age (1-2 Gyr) clusters, the upper envelope of
M67, and NGC 188. This value is comparable to or slightly higher than the
plateau of Pop. II stars. The similarity of the average Li abundance of
clusters of different age and metallicity, along with its closeness to the halo
dwarf plateau, is very intriguing and suggests that, whatever the initial Li
abundance and the Li depletion histories, old stars converge to almost the same
final Li abundance.
