A relativistic generalization of the Lee model is constructed and solved in the first sector. The solubility is achieved with an indefinite metric and a redefinition of antiparticle operators, which amounts to a selection rule prohibiting pair creation. The renormalization of the Vparticle results in three dressed states, one of which is a ghost. The propenties of these states and their dependence on cutoff and coupling strength are discussed. The effects of various modifications of the interaction are analyzed. The N-B scattering problem is solved exactiy. (auth)