The adsorption of Li on Si(111) (coverage below 10(-3) ML) was investigated around the (7x7) to (1x1) phase transition with nuclear magnetic resonance (NMR) and mean residence-time measurements. At the phase transition the local density of states at the Fermi energy drops significantly, indicating a transition from a ''metallic'' surface for the (7x7) reconstruction to a semiconducting surface for the (1x1) one. At the phase transition the activation energy for desorption changes from 2.5 to 2.85 eV. Furthermore, the electric field gradient at the adsorbed Li nucleus, which reflects the surrounding charge distribution, has a discontinuity at the phase transition.