What is offensive about the domain name? Just curious.
Short for "Lolita"?
I don't quite get the original choice of naming outside of perhaps the lack of awareness of cultural subtleties and connotations that underlie cultural appropriation, but it is apt, since choosing to dress in such a way is a voluntary choice to want to be seen and viewed as a (perfect) and very youthful doll more as something to be admired from a distance than to be interacted with—perhaps the notion of sexual immaturity was seen to reinforce Victorian prudishness and vice versa. The way things get verbally abbreviated in Japanese is that they tend to be abbreviated into abbreviations of 2-mora or 4-mora, roughly corresponding to 2 syllables or 4 syllables. Hence Lolita was quickly abbreviated to loli in casual speak.
From there, the usage of the word loli further evolved in Japanese anime-related media. "loli" probably started off as a not-very-common archetype of female character who looked like the idealized lolita dresser—a doll-like prepubescent person with "refined" manners. Perhaps with influence from the original meaning of Lolita, at some point loli was generalized into the (by now common) prepubescent female character archetype in anime-related media, regardless of whether or not the Victorian-motifed dresses accompanied it.