We present the first measurement of cosmic-ray fluxes of ^{6} Li and ^{7} Li isotopes in the rigidity range from 1.9 to 25 GV. The measurements are based on 9.7×10^{5} ^{6} Li and 1.04×10^{6} ^{7} Li nuclei collected by the Alpha Magnetic Spectrometer on the International Space Station from May 2011 to October 2023. We observe that over the entire rigidity range the ^{6} Li and ^{7} Li fluxes exhibit nearly identical time variations and, above ∼4 GV, the time variations of ^{6} Li, ^{7} Li, He, Be, B, C, N, and O fluxes are identical. Above ∼7 GV, we find an identical rigidity dependence of the ^{6} Li and ^{7} Li fluxes. This shows that they are both produced by collisions of heavier cosmic-ray nuclei with the interstellar medium and, in particular, excludes the existence of a sizable primary component in the ^{7} Li flux.