  Using cocycle twists for associative graded algebras, we characterize finite
dimensional nilpotent Lie color algebras $L$ graded by arbitrary abelian groups
whose enveloping algebras $U(L)$ have the property that the injective hulls of
simple right $U(L)$-modules are locally Artinian. We also collect together
results on gradings on Lie algebras arising from this characterization.
