We consider a lattice SU(3) QCD model in 2 + 1 dimensions, with two flavors and 2 × 2 spin matrices. An imaginary time functional integral formulation with Wilson’s action is used in the strong coupling regime, i.e. small hopping parameter \({0 0 }\) , that the bound state masses \({2m-\epsilon_{I\,\pm}}\) are the only points in the mass spectrum in \({(0,2m-\epsilon_{I\,\pm}+\delta \alpha_I\kappa^2)}\) , for I = 0,1, and in \({(0,2m-(1+\delta)\alpha_I\kappa^2)}\) , for I = 2,3. These results are exact and validate our previous results obtained in a ladder approximation. The method employs suitable two- and four-point correlations with spectral representations and a lattice Bethe-Salpeter equation. For I = 0,1, a quark, antiquark space-range one potential of order \({\kappa^2}\) is found to be the dominant contribution to the two-baryon interaction and the interaction of the individual quark isospins of one baryon with those of the other is described by permanents. A novel spectral free decomposition (but spectral representation motivated, for real κ and β) of the two-point correlation, after performing a complex extension, is a key ingredient in showing the joint analyticity of the binding energy.