  Different simplified approaches are used to account for the non-local
thermodynamic equilibrium (NLTE) effects with 3D hydrodynamical model
atmospheres. In certain cases, chemical abundances are derived in 1D NLTE and
corrected for the 3D effects by adding 3D-1D LTE abundance corrections (3D+NLTE
approach). Alternatively, average <3D> model atmospheres are sometimes used to
substitute for the full 3D hydrodynamical models.
  We tested whether the results obtained using these simplified schemes (i.e.,
3D+NLTE, <3D> NLTE) may reproduce those derived using the full 3D NLTE
computations. The tests were made using 3D hydrodynamical CO5BOLD model
atmospheres of the main sequence (MS), main sequence turn-off (TO), subgiant
(SGB), and red giant branch (RGB) stars, all at [M/H]=0.0 and -2.0. Our goal
was to investigate the role of 3D and NLTE effects on the formation of the
670.8 nm lithium line by assessing strengths of synthetic 670.8 nm line
profiles, computed using 3D/1D NLTE/LTE approaches.
  Our results show that Li 670.8 nm line strengths obtained using different
methodologies differ only slightly in most of the models at solar metallicity.
However, the line strengths predicted with the 3D NLTE and 3D+NLTE approaches
become significantly different at subsolar metallicities. At [M/H]=-2.0, this
may lead to (3D NLTE)-(3D+NLTE) differences in the predicted lithium abundance
of ~0.46 and ~0.31 dex in the TO and RGB stars, respectively. On the other
hand, NLTE line strengths computed with the average <3D> and 1D model
atmospheres are similar to those obtained with the full 3D NLTE approach for
MS, TO, SGB, and RGB stars, at all metallicities; 3D-<3D> and 3D-1D differences
in the predicted abundances are always less than ~0.04 dex and ~0.08 dex,
respectively. However, neither of the simplified approaches can reliably
substitute 3D NLTE spectral synthesis when precision is required.
