  Two dimensional angular correlation of the positron annihilation radiation
(2D-ACAR) spectra are measured for $\mathrm{LaB}_6$ along high symmetry
directions and compared with first principle calculations based on density
functional theory (DFT). This allows the modeling of the Fermi surface in terms
of ellipsoid electron pockets centered at $X$-points elongated along the
$\Sigma$ axis (${\Gamma-M}$ direction). The obtained structure is in agreement
with quantum oscillation measurements and previous band structure calculations.
For the isostructural topologically not-trivial $\mathrm{SmB}_6$ the similar
ellipsoids are connected through necks that have significantly smaller radii in
the case of $\mathrm{LaB}_6$. A theoretical analysis of the 2D-ACAR spectra is
also performed for $\mathrm{CeB}_6$ including the on-site repulsion $U$
correction to the local-density approximation (LDA+$U$) of the DFT. The
similarities of 2D-ACAR spectra and the Fermi-surface projections of these two
compounds allow to infer that both $\mathrm{LaB}_6$ and $\mathrm{CeB}_6$ are
topologically trivial correlated metals.
