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We investigate if there is a difference in the lithium abundances of stars belonging to two halo populations of F and G main-sequence stars previously found to differ in [alpha/Fe] for the metallicity range -1.4 < [Fe/H] < -0.7. Li abundances are derived from the LiI 6707.8 A line measured in high-resolution spectra using MARCS model atmospheres. Furthermore, masses of the stars are determined from the logTeff - logg diagram by interpolating between Yonsei-Yale evolutionary tracks. There is no significant systematic difference in the lithium abundances of high- and low-alpha halo stars. For the large majority of stars with masses 0.7 < M/M_sun < 0.9 and heavy-element mass fractions 0.001 < Z < 0.006, the Li 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 abundance close to the primordial value predicted from standard Big Bang nucleosynthesis calculations and the WMAP baryon density. The relation, however, does not apply to stars with [Fe/H] < -1.5. We suggest that metal-rich halo stars were formed with a Li abundance close to the primordial value, and that lithium in their atmospheres has been depleted in time with an approximately linear dependence on stellar mass and Z. The lack of a systematic difference in the Li abundances of high- and low-alpha stars indicates that an environmental effect is not important for the destruction of lithium.