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.
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