The pure rotational spectra of two isotopic species of LuF and three of LuCl have been measured in the frequency range 5-17 GHz using a cavity pulsed jet Fourier transform microwave spectrometer. The samples were prepared by laser ablation of Lu metal in the presence of SF(6) or Cl(2), and stabilized in supersonic jets of Ar. Spectra of molecules in states having v= 0, 1, and 2 have been measured, to produce rotational constants and centrifugal distortion constants, along with hyperfine constants for all the nuclei. Dunham-type fits for LuCl produced a Born-Oppenheimer breakdown parameter for Cl. Although a theoretical calculation showed that Lu in LuCl should have a significant field shift effect parameter, it could not be determined from the spectrum. Equilibrium internuclear distances, r(e), and dissociation energies have been evaluated for both molecules. The nuclear quadrupole coupling constants are discussed in terms of the molecular electronic structure.