In this paper, we generalize construction of Seidel's long exact sequence of
Lagrangian Floer cohomology to that of compact Lagrangian submanifolds with
vanishing Malsov class on general Calabi-Yau manifolds. We use the framework of
anchored Lagrangian submanifolds developed in \cite{fooo:anchor} and some
compactness theorem of \emph{smooth} $J$-holomorphic sections of Lefschetz
Hamiltonian fibration for a generic choice of $J$. The proof of the latter
compactness theorem involves a study of proper pseudoholomorphic curves in the
setting of noncompact symplectic manifolds with cylindrical ends.