In particular, he doesn't address address Massuyeau's comment at all. (Nor does he address an innaccuracy noticed by Dylan Thurston.)

Yes, that's a shame. Do you know of a good reference for simple-homotopy theory that's easier to find?

@Torsten: actually, I changed my mind. That's not cheating. You can certainly get nice quasi-Lie algebras by tensoring graded Lie algebras with $\mathbb Z/2\mathbb Z$. But it would be nice to have examples over $\mathbb Z$ which contain something besides $2$-torsion.

@Peter: that's a fair comment.

@Torsten: yes, that's cheating.

@Torsten: I see what you're saying now.

I don't see what goes wrong if you define a "better" version of the Lie operad by taking the standard Lie operad over the integers, and modding out by symmetric trees of the form [x,x], as Gindi seems to be suggesting. Incidentally, the skew-symmetry axiom defines what's called a quasi-Lie algebra, so the standard Lie operad should really be called the quasi-Lie operad.