  We investigated the electronic structure and superconducting properties of
single-crystalline LaCuSb$_2$. The resistivity, magnetization, and specific
heat measurements showed that LaCuSb$_2$ is a bulk superconductor. The observed
Shubnikov-de Haas oscillation and magnetic field dependence of the Hall
resistivity can be reasonably understood assuming a slightly hole-doped Fermi
surface. Electron-phonon coupling calculation clarified the difference from the
isostructural compound LaAgSb$_2$ indicating that (i) low-frequency vibration
modes related to the interstitial layer sandwiched between the Sb-square nets
significantly contribute to the superconductivity and (ii) carriers with
sizable electron--phonon coupling distribute isotropically on the Fermi
surface. These are assumed to be the origin of higher superconducting
transition temperature compared with LaAgSb$_2$. We conclude that the
superconducting properties of LaCuSb$_2$ can be understood within the framework
of conventional phonon-mediated mechanism.
