Extensions of the recently introduced "Morse/long-range" (MLR) potential function form allow a straightforward treatment of a molecular state for which the inverse-power long-range potential changes character with internuclear separation. Use of this function in a direct-potential-fit analysis of a combination of new fluorescence data for (7,7)Li(2), (6,6)Li(2), and (6,7)Li(2) with previously reported data for the A((1)Sigma(u) (+)) and X((1)Sigma(g) (+)) states yields accurate, fully analytic potentials for both states, together with the analytic "adiabatic" Born-Oppenheimer breakdown radial correction functions which are responsible for the difference between the interaction potentials and well depths for the different isotopologues. This analysis yields accurate well depths of D(e)=8516.709(+/-0.004) and 8516.774(+/-0.004) cm(-1) and scattering lengths of 18.11(+/-0.05) and 23.84(+/-0.05) A for the ground-states of (7,7)Li(2) and (6,6)Li(2), respectively, as well as improved atomic radiative lifetimes of tau(2p)=27.1018(+/-0.0014) ns for (7)Li(2p) and 27.1024(+/-0.0014) ns for (6)Li(2p).