This is a case of the oriented knot complement problem in lens spaces. 

You probably want to avoid reducible examples like that given in Mukherjee’s answer. 

Given that assumption, there is no such example which is irreducible and non hyperbolic by a result of [Daniel Matignon][1]. 

There are examples of cosmetic surgeries on hyperbolic knots in lens spaces that reverse orientation, but I think the orientation preserving case is still open in general.

By the way, maybe the interesting case of this question is for $M$ not a homology circle. Otherwise, the two surgeries must lift to the $p$-fold cyclic cover of $M(r)\cong M(r')\cong L(p,q)$, and hence one would have two surgeries on a knot yielding $S^3$, a contradiction to the knot complement theorem.


  [1]: https://www.google.com/url?sa=t&source=web&cd=13&ved=2ahUKEwidi9XQl9XoAhVEu54KHV8BDt4QFjAMegQIBxAB&url=https%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0166864110000970%2Fpdf%3Fmd5%3D51e697b694602074272e51af2ba3edcf%26pid%3D1-s2.0-S0166864110000970-main.pdf&usg=AOvVaw3DoBvsHZ2Pr7tWvF047sXZ