We present FLAMES/GIRAFFE spectroscopy obtained with the Very Large Telescope (VLT). Using these observations, we have been able (for the first time) to observe the Lii doublet in the main-sequence (MS) stars of a globular cluster. We also observed Li in a sample of subgiant (SG) stars of the same B − V colour. Our final sample is composed of 84 SG and 79 MS stars. In spite of the fact that SG and MS stars span the same temperature range, we find that the equivalent widths of the Lii doublet in SG stars are systematically greater than in MS stars, suggesting a higher Li content among SG stars. This is confirmed by our quantitative analysis, which makes use of both 1D and 3D model atmospheres. We find that SG stars show, on average, a higher Li abundance, by 0.1 dex, than MS stars. We also detect a positive slope of Li abundance with effective temperature: the higher the temperature the higher the Li abundance, both for SG and MS stars, although the slope is slightly steeper for MS stars. These results provide unambiguous evidence that the Li abundance changes with evolutionary state. The physical mechanisms that contribute to this are not yet clear, since none of the proposed models seem to describe accurately the observations. Whether such a mechanism can explain the cosmological lithium problem is still an open question.