  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. The
particle-$\gamma$ 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$\sim$140 region is
discussed. The $^{137,138,139}$La($n, \gamma)$ cross sections were calculated
at $s$- and $p$-process temperatures using the experimentally measured nuclear
level densities and $\gamma$-ray strength functions. Good agreement is found
between $^{139}$La($n, \gamma)$ calculated cross sections and previous
measurements.
