  We use the Lie coalgebra and configuration pairing framework presented
previously by Sinha and Walter to derive a new, left-normed monomial basis for
free Lie algebras (built from associative Lyndon-Shirshov words), as well as a
dual monomial basis for Lie coalgebras. Our focus is on computational dexterity
gained by using the configuration framework and basis. We include several
explicit examples using the dual coalgebra basis and configuration pairing to
perform Lie algebra computations. As a corollary of our work, we get a new
multiplicative basis for the shuffle algebra.
