Title: RG analysis for a weakly self-avoiding Levy walk in the lattice Z^3. Abstract: The Green's function of a (weakly) self-avoiding L\'evy walk in a large but finite cube in Z^3 can be expressed as the two point correlation function in a supersymmetric field theory in this cube. The underlying super-measure has been rigorously analyzed for a particular class of walks by methods of the Wilson RG based on finite range multi-scale expansions. We prove in an appropriate Banach space setup that, for initial parameters of the interaction measuring self-repulsion held in an appropriate domain, there exists a global renormalization group trajectory uniformly bounded on all renormalization group scales and therefore on lattices which become arbitrarily fine. We establish the existence of the critical (stable) manifold. Moreover we prove that interactions are uniformly bounded away from zero on all scales. This is a step in a program to study the critical exponents of of weakly self-avoiding Levy walks. Based on joint work with Benedetto Scoppola published in J.Stat Phys (2008) 133:921-1011.