We study two quotients of the Lie Lie algebra (the Lie algebra of symplectic derivations of the free Lie algebra), namely the abelianization and the the quotient by the Lie algebra generated by degree 1 elements. The abelianization has a very close connection to the homology of groups of automorphism groups of free groups, whereas the second is the so-called "Johnson cokernel," the cokernel of the Johnson homomorphism defined for mapping class groups of punctured surfaces.