Lossy mode resonance (LMR) sensors offer a promising avenue to surpass the constraints of conventional surface plasmon resonance (SPR) sensors by delivering enhanced label-free detection capabilities. A notable edge of LMR over SPR is its excitation potential by both transverse electric (TE) and transverse magnetic (TM) polarized light. Yet this merit remains underexplored due to challenges to achieving high sensing performance under both TM and TE polarization within a singular LMR model. This study introduces a theoretical model for an LMR prism refractive index sensor based on a MgF2-few layer black phosphorus-MgF2 configuration, which can achieve angular sensitivity nearing 90° refractive index unit-1 (RIU-1) for both polarizations. Leveraging the distinct anisotropic nature of black phosphorus, the figure of merit (FOM) values along its two principal crystal axes (zigzag and armchair) show great difference, achieving an impressive FOM of 1.178 × 106 RIU-1 along the zigzag direction under TE polarized light and 1.231 × 104 RIU-1 along the armchair direction under TM polarized light. We also provide an analysis of the electric field distribution for each configuration at its respective resonant conditions. The proposed structure paves the way for innovative applications of anisotropic-material-based LMR sensors in various applications.