The forgetful functor from the category of $\lambda$-rings to that of rings has a right adjoint in the form of the universal $\lambda$ functor $\Lambda$, which is isomorphic to the big Witt vectors functor. But, does the forgetful functor have a left adjoint? Some kind of free $\lambda$-ring functor?
EDIT: I see this as obviously true when I forget all the way down to sets. But, I only want to forget down to the category of commutative rings. Would it just be to take the free ring on all the elements, mod out by the $\lambda$ relations and all the ring relations?