From high-resolution spectroscopy in the Li I λ67O.8 nm region of the double-lined detached eclipsing binary system EK Cepheid, we find a surface lithium abundance in the low-mass (1.12 M0) secondary of log N(Li)NLTE = 3.l±0.3, i.e., close to the present "cosmic" Li abundance. The abundances of Ca, Si and Fe, inferred from metallic lines in the neigbourhood of the Li I line are consistent with solar metallicity. Our results provide new evidence that EK Ceph B is the first known solar-type pre-main sequence (PMS) star with directly determined mass. The position of EK Ceph B in the H-R diagram is marginally consistent (within observational uncertainties) with theoretical predictions for its mass at an age of 20 Myr. However, the lithium abundance of EK Ceph B is not consistent with PMS models that predict Li depletion ≥0.3 dex for 1.1 Msun at 20 Myr. In order to gain some insight of the evolution of lithium for 1.1 Msun stars, we have compared the Li abundance of EK Ceph B with that of Post T Tauri stars and members of αPer and the Pleiades. The Li abundance of EK Ceph B is the same as that of α Per and Pleiades 1.4 Msun stars, for which no Li depletion is expected to occur. The mean Li abundance of Per and Pleiades members with masses around 1. Msun is 0.1 dex. and 0.45 dex. lower, respectively, than that of EK Ceph B. The observations suggest that no significant PMS Li depletion occurs in stars slightly more massive than the Sun, and that a moderate amount of Li depletion takes place after settling on the ZAMS with a short timescale comparable to that of effective surface braking. The first mechanism of Li depletion at 1.1 Msun may be the shear instabilities produced by strong angular momentum loss in the convection region.