For a graph $G$ on $n$ vertices with normalized Laplacian eigenvalues $0 = λ_1(G) \leq λ_2(G) \leq \cdots \leq λ_n(G)$ and graph complement $G^c$, we prove that \begin{equation*} \max\{λ_2(G),λ_2(G^c)\}\geq \frac{2}{n^2}. \end{equation*} We do this by way of lower bounding $\max\{i(G), i(G^c)\}$ and $\max\{h(G), h(G^c)\}$ where $i(G)$ and $h(G)$ denote the isoperimetric number and Cheeger constant of $G$, respectively.