Context : Accurate spectroscopic lithium abundances are essential in addressing a variety of open questions , such as the origin of a uniform lithium content in the atmospheres of metal-poor stars ( Spite plateau ) or the existence of a correlation between the properties of extrasolar planetary systems and the lithium abundance in the atmosphere of their host stars .

Aims : We have developed a tool that allows the user to improve the accuracy of standard lithium abundance determinations based on 1D model atmospheres and the assumption of Local Thermodynamic Equilibrium ( LTE ) by applying corrections that account for hydrodynamic ( 3D ) and non-LTE ( NLTE ) effects in FGK stars of different metallicity .

Methods : Based on a grid of CO5BOLD 3D models and associated 1D hydrostatic atmospheres , we computed three libraries of synthetic spectra of the lithium \lambda 670.8 nm line for a wide range of lithium abundances , accounting for detailed line formation in 3D NLTE , 1D NLTE , and 1D LTE , respectively .
The resulting curves-of-growth were then used to derive 3D NLTE and 1D NLTE lithium abundance corrections .

Results : For all metallicities , the largest corrections are found at the coolest effective temperature , { T _ { eff } } = 5000 K. They are mostly positive , up to +0.2 dex , for the weakest lines ( lithium abundance A ( Li ) _ { 1 DLTE } = 1.0 ) , whereas they become more negative towards lower metallicities , where they can reach -0.4 dex for the strongest lines ( A ( Li ) _ { 1 DLTE } = 3.0 ) at [ Fe/H ] = -2.0 .
We demonstrate that 3D and NLTE effects are small for metal-poor stars on the Spite plateau , leading to errors of at most \pm 0.05 dex if ignored .
We present analytical functions evaluating the 3D NLTE and 1D NLTE corrections as a function of { T _ { eff } } [ 5000 \ldots 6500 K ] , \log g [ 3.5 \ldots 4.5 ] , and LTE lithium abundance A ( Li ) [ 1.0 \ldots 3.0 ] for a fixed grid of metallicities \mathrm { [ Fe / H ] } [ -3.0 \ldots 0.0 ] .
In addition , we also provide analytical fitting functions for directly converting a given lithium abundance into an equivalent width , or vice versa , a given equivalent width ( EW ) into a lithium abundance .
For convenience , a Python script is made available that evaluates all fitting functions for given { T _ { eff } } , \log g , \mathrm { [ Fe / H ] } , and A ( Li ) or EW .

Conclusions : By means of the fitting functions developed in this work , the results of complex 3D and NLTE calculations are made readily accessible and quickly applicable to large samples of stars across a wide range of metallicities .
Improving the accuracy of spectroscopic lithium abundance determinations will contribute to a better understanding of the open questions related to the lithium content in metal-poor and solar-like stellar atmospheres .