We perform non-LTE calculations of lithium in late-type stars for a wide range of stellar parameters, including quantum mechanical cross-sections for collisions with neutral hydrogen and the negative hydrogen ion. Non-LTE abundance corrections for the lithium resonance line at 670.7nm and the subordinate line at 610.3nm, are calculated using 1D MARCS model atmospheres spanning a large grid in effective temperature, surface gravity, and metallicity, and lithium abundance. The competing effects of ultraviolet over-ionization and photon losses in the resonance line govern the behaviour of the non-LTE effects with stellar parameters and lithium abundance. The size and sign of the non-LTE abundance corrections vary significantly over the grid for the 670.7nm line, but are typically positive and below 0.15dex for the 610.3nm line. The new collisional data play a significant role in determining the abundance corrections.