A previous study of F and G main-sequence stars in the solar neighborhood has revealed the existence of two distinct halo populations with a clear separation in [alpha /Fe] for the metallicity range -1.4 < [Fe/H] < -0.7. The kinematics of the stars and models of galaxy formation suggest that the ``high-alpha '' stars were formed in situ in the inner parts of the Galaxy, whereas the ``low-alpha '' ones have been accreted from satellite galaxies. In order to see if there is any systematic difference in the lithium abundances of high- and low-alpha stars, equivalent widths of the iLi 6707.8 Å line have been measured from VLT/UVES and NOT/FIES spectra and used to derive Li abundances. Furthermore, stellar masses are determined from evolutionary tracks in the log T_eff - log g diagram. For stars with masses 0.7 < M/M☉ < 0.9 and heavy-element fractions 0.001 ⪉ Z < 0.006, the lithium abundance is well fitted by a relation A(Li) = a0 + a1 M + a2 Z + a3 M Z, where a0, a1, a2, and a3 are constants. Extrapolating this relation to Z = 0 leads to A(Li)= 2.58 ± 0.08 close to the primordial Li abundance predicted from standard Big Bang nucleosynthesis calculations and the WMAP baryon density. A(Li) of high- and low-alpha stars agrees well, which underlines the universality of the origin of lithium. We suggest that these old halo stars were formed with a lithium abundance close to the primordial value, and that lithium in their atmospheres has been depleted in timea with an approximately linear dependence on Z and stellar mass.