  Given a symplectic manifold $(M^{2n},\omega)$ we study Lagrangian cobordisms
$V\subset E$ where $E$ is the total space of a Lefschetz fibration having $M$
as generic fiber. We prove a generation result for these cobordisms in the
appropriate derived Fukaya category. As a corollary, we analyze the relations
among the Lagrangian submanifolds $L\subset M$ that are induced by these
cobordisms. This leads to a unified treatment - and a generalization - of the
two types of relations among Lagrangian submanifolds of $M$ that were
previously identified in the literature: those associated to Dehn twists that
were discovered by Seidel and the relations induced by cobordisms in trivial
symplectic fibrations described in our previous work.
