  We report state-of-the-art ab initio calculations of the potential energy
curve for the $a^3\Sigma_u^+$ state of the lithium dimer conducted to achieve
spectroscopic accuracy ($<$1cm$^{-1}$) without any prior adjustment to fit the
corresponding experimental data. The nonrelativistic clamped-nuclei component
of the interaction energy is calculated with a composite method involving
six-electron coupled cluster and full configuration interaction theories
combined with basis sets of Slater-type orbitals ranging in quality from
double- to sextuple-zeta. To go beyond the nonrelativistic Born-Oppenheimer
picture we include both the leading-order relativistic and adiabatic
corrections, and find both of these effects to be non-negligible within the
present accuracy standards. The potential energy curve developed by us allowed
to calculate molecular parameters ($D_e$, $D_0$, $\omega_e$ etc.) for this
system, as well as the corresponding vibrational energy levels, with an error
of only a few tenths of a wavenumber ($0.2-0.4\,$cm$^{-1}$). We also report an
ab initio value for the scattering length of two $^2S$ lithium atoms which
determines the stability of the related Bose-Einstein condensate.
