We study biological sensing using the hybridization phase of localized surface plasmon resonances (LSPRs) with diffraction modes (photonic lattice modes) in arrays of gold nanoantennas. We map the degree of the hybridization process using an embedding dielectric material (Si), identifying the critical thicknesses wherein the optical responses of the arrays are mainly governed by pure LSPRs (insignificant hybridization), Fano-type coupling of LSPRs with diffraction orders (hybridization state), and their intermediate state (hybridization phase). The results show that hybridization phase can occur with slight change in the refractive index (RI), leading to sudden reduction of the linewidth of the main spectral feature of the arrays by about one order of magnitude while it is shifted nearly 140 nm. These processes, which offer significant improvement in RI sensitivity and figure of merit, are utilized to detect monolayers of biological molecules and streptavidin-conjugated semiconductor quantum dots with sensitivities far higher than pure LSPRs. We further explore how these sensors can be used based on the uncoupled LSPRs by changing the polarization of the incident light.