An analytic theory is presented for the collisionless. lamentation instability of thin current sheets in the frequency domain of lower-hybrid waves in low-beta plasmas. In a configuration with a strong guide field, the plasma dynamics is studied in a fluid description, accounting for the effects of electron polarization and finite Larmor radii, as well as of the motion of unmagnetized ions in the presence of perpendicular electric fields. In the linear phase, two types of unstable perturbations of a thin current sheet with steep edges are identified that correspond to its filamentation (or tearing) and bending. Using a surface-wave formalism for the modes whose wavelength is larger than the current sheet thickness, the corresponding growth rates are calculated as the contributions of singularities in the dispersion function of surfacewaves. These are governed by the electron inertia and by linear coupling with local plasma modes propagating in the perpendicular direction that are subjected to the Buneman instability. This new linear instability provides a suitable channel for the dissipation of current sheets that evolve during the collisionless magnetic reconnection in shear- and kinetic-Alfven regimes, and for the creation of anomaluos resistivity.