We construct a family of flows indexed by parameters in T2 which contains a Lorenz-like singularity. For each of them, we provide a topological equivalence caracterization and a proof of the existence of invariant stable foliation. We use these results to deduce the existence of a singular-hyperbolic attractor for each member of this family of flows and to classify all the bifurcation parameters μ and the associated attractor. We concluded the existence of a set V ⊂ T2 with non empty interior such that the maximal invariant set Λμ contains a Lorenz attractor and a Smale horseshoe for each μ ∈ V.