According to Richard Frushell, this spelling is often considered to have been made up by Poe for the title character in his short story (not poem). It was most likely derived from Milton's character Ligea in Comus, a work with which with Poe was familiar. Milton, in turn, got the name from Homer's siren in the Odyssey, who was originally named Lambda Iota Gamma Omega Iota Alpha (ligoia).
The girl name Līga comes from the Latvia-indian word which means, "lord of sweetness."