Jet-cooled LiCu has been investigated using resonant two-photon ionization spectroscopy. A long vibrational progression was observed and identified as the [20.5] (1) Sigma(+)<--X-1 Sigma(+) band system. Ten bands of the system were rotationally resolved for (LiCu)-Li-7-Cu-63, giving bond lengths of ro =2.2618(3) Angstrom for the X (1) Sigma(+) state and r(e)’=2.74(4) Angstrom for the [20.5] (1) Sigma(+) state. The fitted spectroscopic parameters of the [20.5] (1) Sigma(+) state were used to obtain a RKR estimate of the [20.5] (1) Sigma(+) potential energy curve. The unusual shape of this curve is thought to derive from avoided crossings between the Li+Cu- ion pair state and covalent states, with the Li+Cu- ion pair state ultimately correlating to the ground electronic state of the molecule.