  We construct a basis for free Lie algebras via a ``left-greedy'' bracketing
algorithm on Lyndon-Shirshov words. We use a new tool -- the configuration
pairing between Lie brackets and graphs of Sinha-Walter -- to show that the
left-greedy brackets form a basis. Our constructions further equip the
left-greedy brackets with a dual monomial Lie coalgebra basis of ``star''
graphs. We end with a brief example using the dual basis of star graphs in a
Lie algebra computation.
