We study the 2S-3S transition of (6,7)Li by high-precision laser spectroscopy using two-photon Doppler-free excitation and photoionization detection. Interferometric cross referencing to metrologic Rb 3S-5D two-photon transitions allowed measurement of the transition isotope shift and hyperfine splitting in the 3S state with precision at the 30 kHz level. The results are IS=11 453.734(30) MHz, A(3S)(6Li)=35.263(15) MHz, and A(3S)(7Li)=93.106(11) MHz. Combined with recent theoretical work, the isotope shift yields a new value for the change in squared nuclear charge radii DeltaR(2)=0.47(5) fm(2). This is compared with other work and some existing discrepancies are resolved.