A model for function spaces

Let f:X→Y be a map between simply connected spaces and f¯:L(V)→L(W) its Quillen model. If the differential on L(V) has only linear and quadratic parts, we show that there is a Lie algebra structure on HomTV(TV⊗(Q⊕sV),L(W)), making of it a Lie model of the function space map(X,Y;f).