We report on finite bias spectroscopy measurements of the two-electron spectrum in a gate defined bilayer graphene (BLG) quantum dot for varying magnetic fields. The spin and valley degree of freedom in BLG give rise to multiplets of 6 orbital symmetric and 10 orbital anti-symmetric states. We find that orbital symmetric states are lower in energy and separated by $approx 0.4 - 0.8$ meV from orbital anti-symmetric states. The symmetric multiplet exhibits an additional energy splitting of its 6 states of $approx 0.15 - 0.5$ meV due to lattice scale interactions. The experimental observations are supported by theoretical calculations, which allow to determine that inter-valley scattering and current-current interaction constants are of the same magnitude in BLG.