New fibre spectroscopy and radial velocities from the WIYN telescope are used to measure photospheric lithium in 242 high-probability, zero-age main-sequence F- to K-type members of the rich cluster M35. Combining these with published rotation periods, the connection between lithium depletion and rotation is studied in unprecedented detail. At T_eff_<5500K there is a strong relationship between faster rotation and less Li depletion, although with a dispersion larger than measurement uncertainties. Components of photometrically identified binary systems follow the same relationship. A correlation is also established between faster rotation rate (or smaller Rossby number), decreased Li depletion and larger stellar radius at a given T_eff_. These results support models where star-spots and interior magnetic fields lead to inflated radii and reduced Li depletion during the pre-main-sequence (PMS) phase for the fastest rotators. However, the data are also consistent with the idea that all stars suffered lower levels of Li depletion than predicted by standard PMS models, perhaps because of deficiencies in those models or because saturated levels of magnetic activity suppress Li depletion equally in PMS stars of similar T_eff_ regardless of rotation rate, and that slower rotators subsequently experience more mixing and post-PMS Li depletion.