Let? L?be a lens space with its standard contact structure.? We construct a "non-linear Maslov index", which associates an integer to any contact isotopy of? L?starting at the identity, and that has certain properties that allows us to use it to prove rigidity properties of? L?as a contact manifold.This is joint work with Gustavo Granja, Milena Pabiniak, and Sheila(Margherita) Sandon, and it follows earlier work of Givental and Theret that applied to real and complex projective spaces.