Let $G$ be a graph on $n$ vertices with diameter $d$. Show that $\lambda_2\geq \frac{1}{nd}$

Question

Here $\lambda_2$ is the second smallest laplacian eigenvalue for the graph. This bound supposedly is trivial, but i have no idea how to get it. Maybe it comes from using the relation $\lambda_2(G) \geq \lambda_2(G\setminus e)$ along the entire diameter? Maybe it is some type of obscure eigentrick?