Carbon-enhanced metal-poor ( CEMP ) stars are believed to show the chemical imprints of more massive stars ( M \gtrsim 0.8 M _ { \odot } ) that are now extinct . In particular , it is expected that the observed abundance of Li should deviate in these stars from the standard Spite lithium plateau . We study here a sample of 11 metal-poor stars and a double-lined spectroscopic binary with -1.8 < [ Fe / H ] < -3.3 observed with VLT/UVES spectrograph . Among these 12 metal-poor stars , there are 8 CEMP stars for which we measure or constrain the Li abundance . In contrast to previous arguments , we demonstrate that an appropriate regime of dilution permits the existence of “ Li-Spite plateau and C-rich ” stars , whereas some of the ” Li-depleted and C-rich ” stars call for an unidentified additional depletion mechanism that can not be explained by dilution alone . We find evidence that rotation is related to the Li depletion in some CEMP stars . Additionally , we report on a newly recognized double-lined spectroscopic binary star in our sample . For this star , we develop a new technique from which estimates of stellar parameters and luminosity ratios can be derived based on a high-resolution spectrum alone , without the need for input from evolutionary models .