In the present work, we study the link between rotation and lithium abundance in giant stars of luminosity class III, on the basis of a large sample of 309 single stars of spectral type F, G and K. We have found a trend for a link between the discontinuity in rotation at the spectral type G0III and the behavior of lithium abundances around the same spectral type. The present work also shows that giant stars presenting the highest lithium contents, typically stars earlier than G0III, are those with the highest rotation rates, pointing for a dependence of lithium content on rotation, as observed for other luminosity classes. Giant stars later than G0III present, as a rule, the lowest rotation rates and lithium contents. A large spread of about five magnitudes in lithium abundance is observed for the slow rotators. Finally, single giant stars with masses 1.5<M/M_{sun}_<=2.5 w a clearest trend for a correlation between rotational velocity and lithium abundance.