We have measured the in-plane energy and angular distributions of scattered Li ϩ ions that result when Li ϩ ion beams with incident energies E i ϭ100 and 400 eV impinge on Cu͑001͒ with an incident angle i ϭ65°and along the ͗100͘ azimuth. By comparing the energy and angular distributions with those generated by classical trajectory simulations, we extract information about the ion-surface interaction potential. A model ion-surface potential consisting of a sum of Hartree-Fock pair potentials and an attractive term produces good agreement with the measured distributions at both incident energies, while the universal potential of Ziegler, Biersack, and Littmarck does so only for E i ϭ 400 eV. Analysis of the simulated distributions enables us to correlate different types of scattering events with features of the measured distributions ͑e.g., rainbows͒ and so obtain a detailed understanding of the scattering of Li ϩ , which is more complex than has been previously observed for heavier alkali ions ͑e.g., Na ϩ and K ϩ ). We find that the energy loss of the Li ϩ ions can be mostly accounted for by momentum transfer to the surface atoms and that inelastic losses are small but significant for this system at these incident energies. We also find that the thermal vibrations of the surface atoms have dramatic effects on the simulated energy and angular distributions.