Modulating the electronic structure is essential for improving the anchoring and catalytic capabilities of catalysts in lithium-sulfur batteries (LSBs). This study delves into the modulation of d-orbitals in transition metal dual-atom catalysts (DACs) supported by boron nitride and graphene (BNC) hybrid sheets for LSBs. This study reveals that the d-band center of the DACs, a key determinant of material chemical properties, is primarily determined by the electronic configuration of the dyz and dx2-y2 orbitals. Furthermore, the interaction between dz2 of transition metals and S_3 p orbitals is critical for the binding strength of LiPSs. By understanding these interactions, the functionality of DACs can be customized for optimal performance in LSBs. For example, the MnCrBNC catalyst with 10 d-electrons exhibits the optimal d-band center and demonstrates exceptional LiPSs binding capability, the lowest Li2S decomposition energy barrier, and the lowest Gibbs free energy of reaction for the rate-determining step of sulfur reduction. This study elucidates the fundamental mechanisms for designing high-performance LSB catalysts through electronic structure modulation.