Context :

Aims : Because of the complexities involved in treating spectral line formation in full 3D and non-local thermodynamic equilibrium ( NLTE ) , different simplified approaches are sometimes used to account for the NLTE effects with 3D hydrodynamical model atmospheres .
In certain cases , chemical abundances are derived in 1D NLTE and then corrected for the 3D effects by adding 3D–1D LTE ( Local Thermodynamic Equilibrium , LTE ) abundance corrections ( 3D+NLTE approach ) .
Alternatively , average \left \langle \mbox { 3 D } \right \rangle model atmospheres are sometimes used to substitute for the full 3D hydrodynamical models .

Methods : In this work we tested whether the results obtained using these simplified schemes ( 3D+NLTE , \left \langle \mbox { 3 D } \right \rangle NLTE ) may reproduce those derived using the full 3D NLTE computations .
The tests were made using 3D hydrodynamical CO ^ { 5 } BOLD model atmospheres of the main sequence ( MS ) , main sequence turn-off ( TO ) , subgiant ( SGB ) , and red giant branch ( RGB ) stars , all at two metallicities , [ \mathrm { 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 resonance line .
This was done by assessing differences in the strengths of synthetic 670.8 nm line profiles , which were computed using 3D/1D NLTE/LTE approaches .

Results : 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 studied here .
However , the line strengths predicted with the 3D NLTE and 3D+NLTE approaches become significantly different at subsolar metallicities .
At [ \mathrm { M / H } ] = -2.0 , this may lead to ( 3D NLTE ) – ( 3D+NLTE ) differences in the predicted lithium abundance of \sim 0.46 and \sim 0.31 dex in the TO and RGB stars respectively .
On the other hand , NLTE line strengths computed with the average \left \langle \mbox { 3 D } \right \rangle 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 ; { 3 D } - \left \langle \mbox { 3 D } \right \rangle and { 3 D } - { 1 D } differences in the predicted abundances are always less than \sim 0.04 dex and \sim 0.08 dex , respectively .
However , neither of the simplified approaches can reliably substitute 3D NLTE spectral synthesis when precision is required .

Conclusions :