We have obtained spectra of the high-lying vibrational levels of the A(1) Sigma(u)(+) and 1(3) Sigma(g)+ states of both Li-6(2) and Li-7(2) via photoassociation of colliding ultracold atoms confined to a magneto-optical trap. Because of the low collision energies (similar to 1 mK), very high spectroscopic resolution is realized, and sensitivity is greatest for the usually difficult to access long-range states. Binding energies relative to the center of gravity of the resolved hyperfine structure are given for the A(1) Sigma(u)(+) vibrational levels v=62-88 for Li-6(2) and v=65-97 for Li-7(2), and the 1(3) Sigma(g)(+) vibrational levels v=56-84 for Li-6(2) and v=62-90 for Li-7(2). These are extremely long-range levels with outer classical turning points ranging from 25 a(0) to 220 a(0), where a(0) is the Bohr radius. The spectra arise mainly from s-wave collisions, and therefore exhibit little rotational structure.