Differential cross sections for the elastic scattering of 350 MeV {sup 7}Li from {sup 12}C and {sup 28}Si have been measured. The characteristics of the angular distributions are very similar to those of 318 MeV {sup 6}Li scattering from the same targets, with diffractive oscillations at the forward angles and smooth exponential falloff, attributed to the dominance of far-side scattering, at the larger angles. The peak-to-valley ratios of the oscillatory structure are similar to those for {sup 6}Li, indicating that the {sup 7}Li ground-state quadrupole moment has no discernible effect on the cross sections. Like the {sup 6}Li data, the {sup 7}Li data define unique phenomenological optical-model potentials. Double-folding model potentials calculated from fundamental nucleon-nucleon interactions also provide reasonably good fits to the experimental data.