  We introduce the notion of K\"ahler manifolds that are almost Einstein and we
define a generalized mean curvature vector field along submanifolds in them. We
prove that Lagrangian submanifolds remain Lagrangian, when deformed in
direction of the generalized mean curvature vector field. For a K\"ahler
manifold that is almost Einstein, and which in addition has a trivial canonical
bundle, we show that the generalized mean curvature vector field of a
Lagrangian submanifold is the dual vector field associated to the Lagrangian
angle.
