Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil on the manifold extending the Morse function to the whole manifold. From this construction, we define a sequence of symplectic invariants classifying the isotopy classes of Lagrangian spheres in a symplectic 4-manifold.
"Lagrangian submanifolds and Lefschetz pencils." J. Symplectic Geom. 3 (2) 171 - 219, June 2005.