Context. 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. Aims. These nine associations, with ages of between about 6 Myr and 70 Myr, 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. Methods. 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. Results. We present the Li depletion as a function of age in the first hundred million years for the first time for the most extended sample of Li abundances in young stellar associations. Conclusions. A clear Li depletion can be measured in the temperature range from 5000 K to 3500 K for the age span covered by the nine associations studied in this paper. The age sequence based on the Li-clock agrees well with the isochronal ages, the Cha association being the only possible exception. The lithium depletion patterns for the associations presented here resemble those of the young open clusters with similar ages, strengthening the notion that the members proposed for these loose young associations have indeed a common physical origin. The observed scatter in the Li abundances hampers the use of Li in determining reliable ages for individual stars. For velocities above 20 km s −1 , rotation seems to play an important role in inhibiting the Li depletion.