  Here we prove that up to diffeomorphism every compact Stein manifold W of
dimension 2n+2>4 admits a Lefschetz fibration over the two-disk with Stein
regular fibers, such that the monodromy of the fibration is a symplectomorphism
induced by compositions of right-handed Dehn twists along embedded Lagrangian
n-spheres on the generic fiber. This generalizes the Stein surface case of n=1,
previously proven by Loi-Piergallini and Akbulut-Ozbagci. More precisely, we
show that up to Liouville isomorphism any Weinstein domain W admits a
compatible compact convex Lefschetz fibration with Weinstein regular fibers and
with the same monodromy description stated above. Moreover, the induced convex
open book supports the induced contact structure on the boundary of W.
