Let $T^\star N$ be the cotangent bundle of some manifold $N$. I think it is a standard fact that, given a $1$-form $\mu$ on $N$, $\text{Graph}(\mu)$ is a Lagrangian submanifold of $T^\star N$.
My question is the following: say I have two Lagrangians $L_1$ and $L_2$ in some symplectic manifold, and I choose a Weinstein neighbourhood $\mathcal{U}$ of $L_1$ (so a neighbourhood in which $L_1$ locally looks like the inclusion of the zero section $L_1 \overset{0}{\hookrightarrow} T^\star L_1$)
Is it possible to find a function $f$ such that, in this neighbourhood, $L_2 = \text{Graph}(\mathrm{d}f)$? (Maybe shrinking the neighbourhood $\mathcal{U}$, if necessary?)