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The measurement of the absolute frequencies of the 2S → 3S of atomic lithium is reported. To reduce systematic effects, we employed a frequency-comb-stabilized excitation laser, a weakly collimated atomic beam, and the cascading 2P → 2S 670 nm fluorescence as the signal. The transition frequencies, including two isotopes (6,7Li), were measured to an accuracy of < 330 kHz. In comparison with the previous GSI Group experiment, the frequency of the 2S1/2 → 3S1/2 transition of 7Li is 815 618 181.45(9) MHz, which is improved by a factor of 2. The resultant hyperfine constants of the 3S state and the deduced difference of the nuclear charge radii δ (Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed) from the isotope shift are in good agreement with previous results. Since a more straightforward methodology is adopted, our measurement is less model dependent and serves as an independent investigation of the reported transitions. [ABSTRACT FROM AUTHOR]