The complete study of the X 1Σ + g ground state of 7Li 2 is performed by laser-induced fluorescence Fourier transform spectrometry. Through several laser excitations either by an Ar + laser or a tunable single-mode ring dye laser, the vibrational levels of the ground state are analyzed up to v′'= 40 and the last bound v′'= 41 level calculated. This extends the known potential curve to R = 12.6 Å, at 2 cm −1 below the dissociation limit (99.975% of the well depth D e). The long-range analysis gives a precise determination of the ground state dissociation limit, D e = 8516.78(54) cm −1, together with long-range parameters C 6 = 5.6(8)×10 6 Å 6 cm −1 and C 8 = 2.3(10)×10 8 Å 8 cm −1 with 2 standard deviations uncertainty. From the observation of the v′' = 40 level, we directly found 8516.24 < D e < 8516.65 cm −1, in good agreement with the extrapolated value.