Lagrangian fillings for Legendrian links of finite type

We prove that there are at least seeds many exact embedded Lagrangian fillings for Legendrian links of type $\mathsf{A}\mathsf{D}\mathsf{E}$. We also provide seeds many Lagrangian fillings with certain symmetries for type $\mathsf{B}\mathsf{C}\mathsf{F}\mathsf{G}$. Our main tools are $N$-graphs and the combinatorics of seed patterns of finite type.