A set of prompt partial γ-ray production cross sections from thermal neutron capture were measured for the La139(n,γ) reaction using a guided beam of subthermal (thermal and cold) neutrons incident on a La2natO3 target at the Prompt Gamma Activation Analysis facility of the Budapest Research Reactor. Absolute La140 cross sections were determined relative to the well-known comparator Cl35(n,γ) cross sections from the irradiation of a stoichiometric LaCl3nat sample. The total cross section for radiative thermal neutron capture on La139 from the sum of experimentally measured cross sections observed to directly feed the La140 ground state was determined to be σ0expt=8.58(50) b. To assess completeness of the decay scheme and as a consistency check, the measured cross sections for transitions feeding the ground state from levels below a critical energy of Ec=285 keV were combined with a modeled contribution accounting for ground-state feeding from the quasicontinuum to arrive at a total cross section of σ0=9.36(74) b. In addition, a neutron-separation energy of Sn=5161.001(21) keV was determined from a least-squares fit of the measured primary γ-ray energies to the low-lying levels of the La140 decay scheme. Furthermore, several nuclear structure improvements are proposed for the decay scheme. The measured cross-section and separation-energy results are comparable to earlier measurements of these quantities.