  In this paper we classify symplectic Lefschetz fibrations (with empty base
locus) on a four-manifold which is the product of a three-manifold with a
circle. This result provides further evidence in support of the following
conjecture regarding symplectic structures on such a four-manifold: if the
product of a three-manifold with a circle admits a symplectic structure, then
the three-manifold must fiber over a circle, and up to a self-diffeomorphism of
the four-manifold, the symplectic structure is deformation equivalent to the
canonical symplectic structure determined by the fibration of the
three-manifold over the circle.
