The story
The first known uses of lily-livered are in William Shakespeare’s works written c. 1603–1606; see quotations below. From the medieval belief that the liver was the seat of courage, and the pale color of the lily flower. A person who had no blood in their liver would have no courage and would thus be a coward. Equivalent to lily + livered.
Etymology from Wiktionary, CC BY-SA 4.0.