We obtained low- to intermediate-resolution (R~2500-9000) optical (~560-770nm) spectra of two mid-L subdwarfs, SDSS J125637.13-022452.4 (SDSS1256; sdL3.5) and 2MASS J162620.14+392519.5 (2MASS1626; sdL4). We report the presence of a feature at the nominal position of the lithium absorption doublet at 6707.8{AA} in the spectrum of SDSS1256, with an equivalent width of 66+/-27{AA} 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+/-10km/s and -239+/-12km/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{AA} 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.