The potential energy curve for the B (1)Pi(u) state of Li-2 has a rotationless barrier which protrudes above its energy asymptote. A direct fit to spectroscopic data for all three isotopomers of this species, including Lambda-doubling splittings and tunneling predissociation line widths, is used to determine an accurate analytic potential energy function plus Born-Oppenheimer breakdown and Lambda-doubling perturbation radial strength functions for this system. This analysis introduces an analytic model for representing a potential function with a rotationless barrier, and shows that a radial perturbation function treatment can determine the symmetry of the perturbing state giving rise to Lambda-doubling splittings. (C) 2003 American Institute of Physics.