Mirror symmetry is a duality between the symplectic geometry of a Calabi-Yau manifold $X$ and the complex geometry of its mirror $\check{X}$. In particular, special Lagrangians in the Calabi-Yau $X$ are mirror to semi-stable sheaves on $\check{X}$. In a joint work with Shih-Kai Chiu, we constructed special Lagrangians in Calabi-Yau $3$-folds with Lefschetz K3-fibrations from the geodesics with respect to certain quadratic differentials on the base. The phenomenon is similar to the holomorphic curves degenerating to tropical curves at toric degenerations and conjectured by Donaldson-Scaduto. We will then discuss some consequences on the Donaldson-Thomas invariants assuming mirror symmetry.