A nonlocal two-fluid formulation has been constructed for describing lower-hybrid drift instabilities in current-sheet configuration with a finite guide magnetic field in the context of magnetic reconnection. As a benchmark and verification, a class of unstable modes with multiple eigenstates are found by numerical solutions with guide field turned off. It is found that the most unstable modes are the electrostatic, short-wavelength perturbations in the lower-hybrid frequency range, with wave functions localized at the edge of the current sheet where the density gradient reaches its maximum. It is also found that there exist electrostatic modes located near the center of the current sheet where the current density is maximum. These modes are low-frequency, long-wavelength perturbations. Attempts will be made to compare the current results with those from kinetic theory in the near future since the validity of the fluid theory ultimately needs to be checked with the more fundamental kinetic theory.