We discuss the generalized Lagrange structure of a deformed Minkowski space (DMS), M? , namely a (four-dimensional) generalization of the (local) space-time based on an energy-dependent "deformation" of the usual Minkowski geometry. In M? , local Lorentz invariance is naturally violated, due to the energy dependence of the deformed metric. Moreover, the generalized Lagrange structure of M? allows one to endow the deformed space-time with both curvature and torsion.