  We have investigated electronic structures and phonon spectra of newly
discovered isostructural superconductors LaNiBN (T_c = 4.1 K) and LaPtBN (T_c =
6.7 K). We have found that their electronic structures are substantially
three-dimensional, leading to metallicity both in NiB (PtB) and the intervening
LaN layers. Our ab initio phonon calculations show that almost all phonon modes
contribute to the electron-phonon coupling (EPC) mechanism, reflecting that
both layers are involved in the superconductivity. For LaNiBN, we obtain an EPC
strength of \lambda = 0.52 and a logarithmically averaged characteristic phonon
frequency of \omega_{log} = 376 K, leading to T_c = 3.9 K. Compared with the Ni
B_{1g} mode in LaNiBN, the Pt B_{1g} mode in LaPtBN is reduced by ~70%, leading
to a slightly enhanced \lambda = 0.56 and an ~20 % reduced \omega_{log}. The
estimated T_c is 5.4 K for LaPtBN, in good agreement with the experiment. We do
not find any indication of magnetic instability for either LaNiBN or LaPtBN,
which implies that both systems are EPC mediated superconductors. Further, we
have found an interesting trend of monotonic increase of T_c with respect to
the boron height in the NiB (PtB) layer of both borocarbide and boronitride
superconductors, which suggests a possible way to enhance T_c in these systems.
