In this paper, we discuss the use of Resonance Ionization Mass Spectrometry (RIMS) to perform isotopically selective saturation spectroscopy of lutetium isotopes. Utilizing this technique, it is shown that accurate measurements of the relative frequencies of hyperfine (HF) components for different isotopes easily can be made without the need for an isotopically enriched sample. The precision with which the HF splitting constants can be determined is estimated to be approx.5 times greater than in previous work