Optical frequencies of the D lines of Li6,7 were measured with a relative accuracy of 5×10⊃-11 using an optical comb synthesizer. Quantum interference in the laser induced fluorescence for the partially resolved D2 lines was found to produce polarization dependent shifts as large as 1MHz. Our results resolve large discrepancies among previous experiments and between all experiments and theory. The fine-structure splittings for Li6 and Li7 are 10052.837(22)MHz and 10053.435(21)MHz. The splitting isotope shift is 0.599(30)MHz, in reasonable agreement with recent theoretical calculations. © 2011 American Physical Society.