  Structural, electronic, vibrational and dielectric properties of LaBGeO$_5$
with the stillwellite structure are determined based on \textit{ab initio}
density functional theory. The theoretically relaxed structure is found to
agree well with the existing experimental data with a deviation of less than
$0.2\%$. Both the density of states and the electronic band structure are
calculated, showing five distinct groups of valence bands. Furthermore, the
Born effective charge, the dielectric permittivity tensors, and the vibrational
frequencies at the center of the Brillouin zone are all obtained. Compared to
existing model calculations, the vibrational frequencies are found in much
better agreement with the published experimental infrared and Raman data, with
absolute and relative rms values of 6.04 cm$^{-1}$, and $1.81\%$, respectively.
Consequently, numerical values for both the parallel and perpendicular
components of the permittivity tensor are established as 3.55 and 3.71 (10.34
and 12.28), respectively, for the high-(low-)frequency limit.
