In this contribution, we describe the use of graphene as an efficient catalyst support and the role it plays in increasing the Lewis acidity of the supported metal complexes. By a density functional theory study, we show that the [La(N(SiMe ) ) ] complex can be easily grafted on graphene-OH and -COOH functionalized surfaces. Two stable mono-grafted compounds, (gO)-[La(N(SiMe ) ) ] and (gOO)-[La(N(SiMe ) ) ], are formed, behaving as stronger Lewis acids than the previously reported silica grafted analogues. To study the role of the graphene support in catalysis, we also computed the catalytic activity of the alkylated (gO)-[La(CH ) ] and (gOO)-[La(CH ) ] complexes in the ethylene and 1,3-butadiene homo- and co-polymerization reactions. Both compounds are efficient catalysts for the homo-polymerization of the ethylene and 1,3-butadiene. For the 1,3-butadiene homo-polymerization, the stereoselectivity outcome of the reaction differs according to the grafting site. The results computed for the co-polymerization reaction, finally, show that the high stability of the allylic products leads to the formation of block copolymers.