Summary: We obtain the low-lying energy-momentum spectrum for the imaginary-time lattice four-Fermi or Gross-Neveu model in \(d + 1\) space-time dimensions (\(d = 1,2,3\)) and with \(N\)-component fermions. Let \(0<\kappa\ll 0\) the four-fermion coupling, \(m > 0\) the bare fermion mass and take \(s \times s\) spin matrices \((s = 2,4)\). Our analysis of the one and the two-particle spectrum is based on spectral representation for suitable two- and four-fermion correlations. The one-particle energy-momentum spectrum is obtained rigorously and is manifested by \(\frac{sN}{2}\) isolated and identical dispersion curves, and the mass of particles has asymptotic value order \(-ln \kappa \). The existence of two-particle bound states above or below the two-particle band depends on whether Gaussian domination does hold or does not, respectively. Two-particle bound states emerge from solutions to a lattice Bethe-Salpeter equation, in a ladder approximation. Within this approximation, the \((\frac{sN}{2}-1)\frac{sN}{4}\) identical bound states have \(\mathcal O(\kappa^0)\) binding energies at zero system momentum and their masses are all equal, with value \(\approx -2 \ln \kappa \). Our results can be validated to the complete model as the Bethe-Salpeter kernel exhibits good decay properties.