Hmmm, interesting thought. I found the following links that might support your idea:
Name
Elysia, origin Greek, meaning "struck by lightning":
http://babynamesworld.parentsconnect.com/meaning_of_Elysia.htmlScroll down: Etymology: Elysium is an obscure name that evolved from a designation of a place or person struck by lightning, enelysion, enelysios.
http://www.answers.com/topic/elysiumThe following site gives both meanings (from Elysium, and from
Elisabeth):
http://www.thinkbabynames.com/meaning/0/ElysiaBut this site gives more interesting possibilities:
Elysia - Meaning of the name:
[ 4 syll. e-ly-sia, el-ys-ia ] The girl name
Elysia is pronounced ahLIHZHiyah or ahLIYZHah †.
Elysia has its origins in the Germanic, Hebrew, and Old Greek languages. It is used largely in the English language. From Old Greek roots, its meaning is 'blissful'. In
Roman and Greek mythology, the Latin Elysium or Greek Elysion was the final resting place of the souls of the heroic and the virtuous; this was a pagan concept associated with the
Christian Heaven.
Elysia could be derived as the feminine form of this name. It could also be from
Alicia,
Elizabeth, or the combination of
Elise and
Alicia:
http://www.babynamespedia.com/meaning/Elysia