The A 1 Sigma(u)(+) state of Li-7(2) has been studied using all optical triple resonance spectroscopy. Vibrational levels v=27-62 and rotational levels ranging from J=0 to 27 have been observed. This represents a region between previous data from single photon experiments and new data from cold atom photoassociative spectroscopy. Our data was fit to a Dunham expansion and the resulting molecular constants reproduce most observed energies to within 0.050 cm(-1). A Rydberg-Klein-Rees potential curve has also been constructed and the calculated eigenvalues are in good agreement with observed energies.