In the paper 'Special Lagrangians, stable bundles and mean curvature flow' by R. P. Thomas and S.-T. Yau, page 2. They said

A Lagrangian submanifold $L$ of the Calabi-Yau manifold $(X,\Omega)$, we get an induced volume form $vol$ on $L$, and by a short calculation $\Omega_L=e^{i\theta}dvol_L$. And By Lagrangian we will always mean graded Lagrangian (thus the Maslov class of the Lagrangian, which is the class of $d\theta$ in $H^1(L; 2\pi Z)$, is assumed to vanish, and we have chosen a lift of $\theta$).

Can anyone tell we how a short calculation to getting $\Omega_L=e^{i\theta}dvol_L$. How to lift and getting the zero Maslov class.