Our study is a follow-up of the SACY project, an extended survey in the Southern Hemisphere targeted to search for young nearby associations. Nine associations have either been newly identified, or had their member list better defined. These associations, with ages between about 6 Myr and 70 Myr, form an excellent sample to study the Li depletion in the pre-main sequence (PMS) evolution. We investigate the use of Li abundances as an independent clock to constrain the PMS evolution. We have calculated the LTE Li abundances for 376 members of different young associations. In addition we considered the effects of their projected stellar rotation. We present the Li depletion as 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. A clear Li depletion can be measured in the temperature range from 5000K to 3500K for the age span covered by these nine associations. The age sequence based on the Li-clock agrees well with the isochronal ages, $epsilon$Cha association being the only possible exception. The lithium depletion patterns for those associations resemble those of the young open clusters, 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 to determine reliable ages for individual stars. Rotation velocities above 20 km s$^{-1}$ seem to inhibit the Li depletion.
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