[en] Cross sections of the ¹³⁹La(γ,n) and ¹⁴¹Pr(γ,n) reactions were measured using quasi-monochromatic γ-ray beams from laser Compton scattering. The results are compared to the predictions of Hauser-Feshbach statistical calculations using different models for the γ-ray strength function. The model parameters are constrained by the present experimental data and used to estimate the stellar photoneutron rates and their associated uncertainties and to study the implication for the production of the rare odd-odd nuclide ¹³⁸La by the p process. No evidence for a large thermonuclear p-process contribution to the solar ¹³⁸La is found. The need to further explore the photodestruction rate of ¹³⁸La is emphasized