AbstractWe present the largest sample available to date of lithium abundances in extremely metal poor (EMP) Halo dwarfs. Four T_eff estimators are used, including IRFM and Hα wings fitting against 3D hydrodynamical synthetic profiles. Lithium abundances are computed by means of 1D and 3D-hydrodynamical NLTE computations. Below [Fe/H]~−3, a strong positive correlation of A(Li) with [Fe/H] appears, not influenced by the choice of the Teff estimator. A linear fit finds a slope of about 0.30 dex in A(Li) per dex in [Fe/H], significant to 2–3 σ, and consistent within 1 σ among all the T_eff estimators. The scatter in A(Li) increases significantly below [Fe/H]~−3. Above, the plateau lies at 〈A(Li)_{3D, NLTE}〉 = 2.199 ± 0.086. If the primordial A(Li) is the one derived from standard Big Bang Nucleosynthesis (BBN), it appears difficult to envision a single depletion phenomenon producing a thin, metallicity independent plateau above [Fe/H] = −2.8, and a highly scattered, metallicity dependent distribution below.