The low-lying dipole strength distributions of the odd-mass isotopes {sup 139}La and {sup 141}Pr were studied in nuclear resonance fluorescence experiments using bremsstrahlung beams. Excited states were observed at excitation energies up to 4 MeV. Spectroscopic information was obtained on excitation energies, decay widths, decay branching ratios, and transition probabilities. The states belonging to the [[2{sup +}(multiply-in-circle sign)3{sup -}](multiply-in-circle sign)particle/hole] coupling were a special focus, and the results are compared with other stable odd-mass nuclei at or near the N=82 shell closure.