We present the largest sample available to date of lithium abundances in extremely metal poor (EMP) Halo dwarfs. Four Teff 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 Teff 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.