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This paper explicitly provides two exhaustive and infinite families of pairs (M, k), where M is a lens space and k is a non-hyperbolic knot in M, which produces a manifold homeomorphic to M, by a non-trivial Dehn surgery. Then, we observe the uniqueness of such knot in such lens space, the uniqueness of the slope, and that there is no preserving homeomorphism between the initial and the final M's. We obtain further that Seifert fibered knots, except for the axes, and satellite knots are determined by their complements in lens spaces. An easy application shows that non-hyperbolic knots are determined by their complement in atoroidal and irreducible Seifert fibered 3-manifolds.

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If an irreducible manifold M admits two Dehn fillings along distinct slopes each filling resulting in a reducible manifold, then we call these bireducible Dehn fillings. The first example of bireducible Dehn fillings is due to Gordon and Litherland. More recently, Eudave-Muñoz and Wu presented the first infinite family of manifolds which admit bireducible Dehn fillings. We present another infinite family of hyperbolic manifolds which admit bireducible Dehn fillings. The manifolds obtained by the fillings are always the connect sum of two lens spaces.