The "Goth" part of its name seems to refer to Gothic subculture, with the "ita" being a reference to Lolita. Hence the reference to the popular fashion in Japanese Harajuku culture, 'Gothic Lolita.' "Ita" is also a phrase used in Lolita circles to describe a person who is "doing it wrong". This trends follows similarly in the 'Goth' family.
Lolita is also a term for provocative young girls. The origin of this term was probably used shortly after the publication of Vladamir Nabakov's novel "Lolita".