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The nuclear level densities and $\gamma$-ray strength functions of$^{138,139,140}$La were measured using the $^{139}$La($^{3}$He, $\alpha$),$^{139}$La($^{3}$He, $^{3}$He$^\prime$) and $^{139}$La(d, p) reactions. Theparticle-$\gamma$ coincidences were recorded with the silicon particletelescope (SiRi) and NaI(Tl) (CACTUS) arrays. In the context of theseexperimental results, the low-energy enhancement in the A$\sim$140 region isdiscussed. The $^{137,138,139}$La($n, \gamma)$ cross sections were calculatedat $s$- and $p$-process temperatures using the experimentally measured nuclearlevel densities and $\gamma$-ray strength functions. Good agreement is foundbetween $^{139}$La($n, \gamma)$ calculated cross sections and previousmeasurements.

$^{137,138,139}$La($n$, $\gamma$) cross sections constrained with statistical decay properties of $^{138,139,140}$La nuclei