Our study is a follow-up of the SACY project, an extended high spectral resolution survey of more than two thousand optical counterparts to X-ray sources in the southern hemisphere targeted to search for young nearby association. Nine associations have either been newly identified, or have had their member list revised. Groups belonging to the Sco-Cen-Oph complex are not considered in the present study. These nine associations, with ages of between about 6Myr and 70Myr, form an excellent sample to study the Li depletion in the pre-main sequence (PMS) evolution. In the present paper, we investigate the use of Li abundances as an independent clock to constrain the PMS evolution. Using our measurements of the equivalent widths of the Li resonance line and assuming fixed metallicities and microturbulence, we calculated the LTE Li abundances for 376 members of various young associations. In addition, we considered the effects of their projected stellar rotation.