Out of curiosity, if all of these statements are true, why is Lolithrone or whatever it's called not taken down?
At a guess, there could several reasons:
1) You'd need a lawyer to send a proper Cease&Desist and that costs a pretty penny. (She could probably afford it though.)
2) She doesn't care enough to take action against it.
3) Probably not making any money off of it and/or popular enough to be a competitor.
4) There's some good will involved.
5) I don't know.
The license specifically says any and all content made for this game is ultimately hers but she does try to credit mod authors so there's at least some degree of good faith there. Not sure the same extends to Lolithrone since it allows underage content, which she is vehemently against (unless that's just talk to avoid legal repercussions on her end...)
Nevertheless, the point I was trying to make is that you CAN make your own mods or even a modded version of LT but you do so at your own risk. There's nothing stopping Inno from pulling the rug under your feet; either claiming your content for herself or sending you a
DMCA C&D. Will she do it? Maybe. Maybe not. It would be an a-hole move and word would spread, which in turn would hurt her rep, but low-risk isn't the same as risk-free.
It would be an absolute kick in the balls to spend countless hours doing your own version only for it to be taken down for legal reasons.