Blake's poems are cryptic and invite multiple interpretations. To my amazement, while researching this question I found that the 26 stanzas of these two poems inspired, among other things, an academic paper that runs to 154 pages!
So, as you might expect, there are a lot of theories. Most of them relate in some way to Greek mythology, which is a continuing theme in Blake's poems.
One is that Lyca's name is derived from a Greek word, Laikos, meaning "harlot". In this interpretation, one can see a certain amount of sexuality in the poems, especially the first one. Lyca is said to be "lovely", and there are references to her "bosom" and her "naked"[ness]. It is possible to read the whole thing as a parable for the awakening of female sexuality, with the Lion representing masculinity.
Another potential Greek root is the word for "light". I was unable to find the Greek etymology here, but it may be "Lampo" meaning to glitter or shine. In this interpretation, the light is that associated with purity, and possibly even immortality. We know from Lost that Lyca is a virgin and the ending of Found hints at a certain timelessness.
It is interesting that these poems are not the only places we find the name Lyca. One source confirms that the name is "invented, classical in type" but also that Blake used it in the draft of another poem, Laughing Song. This uses the same AABB rhyme scheme as the Little Girl poems, but is much more lighthearted and positive in tone, concerning itself with the pleasure of the natural world in springtime.
Although I can find no direct connection to the name, one theory is that Lyca represents the Greek goddess Persephone, the personification of Spring. In her legend she is abducted by Hades, the God of the underworld, leading to her mother, Demeter, searching the earth for her. It's not hard to see the parallels between this narrative and that of Lost and Found, nor to the spring theme of Laughing Song.
It is notable that the heroine of Philip Pullman's His Dark Materials trilogy is called Lyra. Pullman has confirmed that Blake's work was influential on the books and the close similarity between the two names and their respective roles in symbolising the loss of innocence is impossible to ignore.
- William Blake: Selected Poetry and Prose, ed. Fuller, D.
- The Name of Blake's Lyca Re-Examined; Peterfreund, Stuart; American Notes & Queries; May 75, Vol. 13 Issue 9, p133
- Blake's "The Little Girl Lost": An Initiation into Womanhood; Greco, Norma A.; Colby Quarterly; Vol 19, Issue 3
- Raine, Kathleen. "The Little Girl Lost and Found and the Lapsed Soul."; The Divine Vision: Studies in the Poetry and Art of William Blake; ed. Vivian de Sola Pinto, 1968.
