Context :

Aims : The aim of the project is to search for lithium in absorption at 6707.8Å to constrain the nature and the mass of the brightest low-metallicity L-type dwarfs ( refered to as L subdwarfs ) identified in large-scale surveys .

Methods : We obtained low- to intermediate-resolution ( R \sim 2500–9000 ) optical ( \sim 560–770 nm ) spectra of two mid-L subdwarfs , SDSS J125637.13 - 022452.4 ( SDSS1256 ; sdL3.5 ) and 2MASS J162620.14 + 392519.5 ( 2MASS1626 ; sdL4 ) with spectrographs on the European Southern Observatory Very Large Telescope and the Gran Telescopio de Canarias .

Results : We report the presence of a feature at the nominal position of the lithium absorption doublet at 6707.8Å in the spectrum of SDSS1256 , with an equivalent width of 66 \pm 27Å at 2.4 \sigma , which we identify as arising from a CaH molecular transition based on atmosphere models .
We do not see any feature at the position of the lithium feature in the spectrum of 2MASS1626 .
The existence of overlapping molecular absorption sets a confusion detection limit of [ Li/H ] = - 3 for equivalently-typed L subdwarfs .
We provided improved radial velocity measurements of - 126 \pm 10 km s ^ { -1 } and - 239 \pm 12 km s ^ { -1 } for SDSS1256 and 2MASS1626 , respectively , as well as revised Galactic orbits .
We implemented adjusting factors for the CaH molecule in combination with the NextGen atmosphere models to fit the optical spectrum of SDSS1256 in the 6200–7300Å range .
We also estimate the expected Li abundance from interstellar accretion ( [ Li/H ] = - 5 ) , place limits on circumstellar accretion ( 10 ^ { 9 } g/yr ) , and discuss the prospects of Li searches in cooler L and T subdwarfs .

Conclusions :