It was proven in [4] that every Lagrangian submanifold M of a complex space form M˜n(4c) of constant holomorphic sectional curvature 4c satisfies the following optimal inequality: δ(2,n−2)≤[Formula presented]H2+2(n−2)c, where H2 is the squared mean curvature and δ(2,n−2) is a δ-invariant on M. In this paper we classify Lagrangian submanifolds of complex space forms M˜n(4c), n≥5, which satisfy the equality case of this improved inequality at every point.