Magnetization measurements are reported on single crystals of dilute Tb, Dy, Ho, or Er in Lu. These measurements were performed in the temperature range 1.5-100 K and field range 0-6 T and include measurements of initial susceptibility, isothermal and isofield magnetization, and basal-plane anisotropy. The results show features similar to the corresponding Y-R alloys, where R is a rare earth. Crystal-field and molecular-field parameters could be unabiguously deduced from the experimental data. The effects of crystal-field level broadening were investigated and demonstrated for Ho. Comparison of the Y-R and Lu-R results makes possible an estimate of the crystal-field parameters in the pure-rare-earth metals.