Thin target L-Shell x-ray production cross sections for protons incident on ₆₂Sm and ₇₀Yb in the energy range of 0.3 to 2.4 MeV/amu, alpha particles incident on ₆₂Sm, ₇₀Yb, and ₈₂Pb in the energy range of 0.15 to 4.8 MeV/amu, and lithium ions incident on ₅₈Ce, ₆₀Nd, ₆₂Sm, ₆₆Dy, ₆₇Ho, ₇₀Yb, and ₈₂Pb in the energy range of 0.8 to 4.4 MeV/amu have been measured. The cross section data have been compared to the planewave Born approximation (PWBA) and the PWBA modified to include binding energy and Coulomb deflection effects. The Lα₁,₂ x-ray production cross sections are best represented by the PWBA modified to include both the binding energy and Coulomb deflection effects (PWBA-BC) over the entire incident ion, incident energy, and target ranges studied. However, the Lγ₁ and Lγ₂,₃,₍₆₎ x-ray production cross sections are best represented by the PWBA except at the lower ion energies, where both the PWBA and PWBA-BC are in disagreement with the data. The comparison of Lα₁,₂/Lγ₂,₃,₍₆₎ ratios to theory reveals that the PWBA-BC does not predict the inflection point substantiated by the data, and the agreement between the data and the PWBA-BC becomes worse as the atomic number of the incident ion increases. Comparison of the PWBA modified to include binding energy effects CPWBA-B) and the PWBA modified to include Coulomb deflection effects (PWBA-C) to the Lα₁,₂, Lγ₁, and the Lγ₂,₃ cross sections for protons, alpha particles, and lithium ions incident on ₇₀Yb indicates that the PWBA-C overestimates the magnitude of the data but does describe the shape of the L₁-associated cross section while the PWBA-B underestimates the magnitude of the data but fails to predict the proper shape of the L₁-associated data. In order to evaluate the ability of the PWBA and the presently accepted modifications to the PWBA to fit the experimental data, future experimentation should be conducted in the energy range that includes the point where the ratio of the incident ion velocity to the L-Shell electron velocity is equal to 0.19 (i.e., V₁/Vₗ = 0.19). This is where the L₁-associated cross sections begin to exhibit the shouldered structure and the cross section ratios L₃/L₁ and L₂/L₁ have inflection points.