The aim of the project is to search for lithium in absorption at 6707.8 Angstroms 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. We obtained low- to intermediate-resolution (R~2500-9000) optical (~560-770 nm) spectra of two mid-L subdwarfs, SDSSJ125637.13-022452.4 (SDSS1256; sdL3.5) and 2MASSJ162620.14+392519.5 (2MASS1626; sdL4) with spectrographs on the European Southern Observatory Very Large Telescope and the Gran Telescopio de Canarias. We report the presence of a feature at the nominal position of the lithium absorption doublet at 6707.8 Angstroms in the spectrum of SDSS1256, with an equivalent width of 66+/-27 Angstroms 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+/-10 km/s and -239+/-12 km/s 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 6200-7300 Angstroms 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.
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