Globular clusters (GCs) are among the oldest objects in the universe. By studying their Li content, insights can be gained about both the cosmological Lithium problem — namely the discrepancy between the Li abundance predicted by standard big bang nucleosynthesis coupled with the baryonic density measured by WMAP and the constant value observed in warm metal poor halo stars, i.e. the Spite plateau — and about the ubiquitous multi-population identified in GCs and, hence, about their chemical enrichment history. I will present the results of two spectroscopic campaigns aimed at studying the Li content of unevolved stars in the GCs ωCen and M4. Additionally, I will also present the results of a search for Li-rich giants among thick disk stars and stars belonging to the Sagittarius dwarf spheroidal galaxy tidal streams. An overall dilution of the stellar lithium content happens as soon as a star evolve off the main sequence. Nevertheless, a few percent of giant stars present high lithium abundances, whose origin is not yet completely understood, at least for low mass stars.