  Accurately known stellar lithium abundances may be used to shed light on a
variety of astrophysical phenomena such as Big Bang nucleosynthesis, radial
migration, ages of stars and stellar clusters, and planet engulfment events. We
present a grid of synthetic lithium spectra that are computed in non-local
thermodynamic equilibrium (NLTE) across the STAGGER grid of three-dimensional
(3D) hydrodynamic stellar atmosphere models. This grid covers three Li lines at
610.4 nm, 670.8 nm, and 812.6 nm for stellar parameters representative of
FGK-type dwarfs and giants, spanning $T_{\rm{eff}}=4000$-7000 K, $\log
g=1.5$-5.0, $[\rm{Fe}/\rm{H}] = -4.0$-0.5, and $\textrm{A(Li)} = -0.5$-4.0. We
find that our abundance corrections are up to 0.15 dex more negative than in
previous work, due to a previously overlooked NLTE effect of blocking of UV
lithium lines by background opacities, which has important implications for a
wide range of science cases. We derive a new 3D NLTE solar abundance of
$\textrm{A(Li)} = 0.96 \pm 0.05$, which is 0.09 dex lower than the commonly
used value. We make our grids of synthetic spectra and abundance corrections
publicly available through the Breidablik package. This package includes
methods for accurately interpolating our grid to arbitrary stellar parameters
through methods based on Kriging (Gaussian process regression) for line
profiles, and MLP (Multi-Layer Perceptrons, a class of fully connected
feedforward neural networks) for NLTE corrections and 3D NLTE abundances from
equivalent widths, achieving interpolation errors of the order 0.01 dex.
