A superconducting state of lithium has not been found at ambient pressure, but the present theoretical work shows that high values of the critical temperature, T(c), may be expected for some high-pressure phases. Ab initio electronic structure calculations are used to calculate the electron-phonon coupling in a "rigid-muffin-tin approximation," and estimates using McMillan's formula suggest that under increasing pressure T(c) in fcc-Li may reach 50--70 K before transitions occur to the rhombohedral (hR1-Li) and subsequently to the cI16-Li phase near 40 GPa. In cI16-Li T(c) may reach a maximum in the range 60--80 K.