The nuclear level densities and γ-ray strength functions of La138,139,140 were measured using the La139(He3,α), La139(He3,He3′), and La139(d,p) reactions. The particle-γ coincidences were recorded with the silicon particle telescope (SiRi) and NaI(Tl) (CACTUS) arrays. In the context of these experimental results, the low-energy enhancement in the A∼140 region is discussed. The La137,138,139(n,γ) cross sections were calculated at s- and p-process temperatures using the experimentally measured nuclear level densities and γ-ray strength functions. Good agreement is found between La139(n,γ) calculated cross sections and previous measurements.