  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 grid Teff=[4000,8000]K, log(g)=[1.0,5.0], and [Fe/H]=[0.0,-3.0], for
lithium abundances in the range A(Li)=[-0.3,4.2]. 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.
