I'm just following this train of thought here suggested by previous posters that LL could be her Chinese name.
Four_seasons is right. LL as initials for a Chinese name just won't work with the Chinese name of Elisa's that's been published all over Chinese news media.
The only other possibility I can think of for the idea that LL is her name initials in some form or another... is that it might be a nickname In Cantonese. I'm of Chinese (specifically Cantonese) descent, just like Elisa, and I've been given a nickname by my family (which is a 2 character nickname, the 1st character is a character from my actual Chinese name pronounced in the Cantonese dialect, and the 2nd character is just another Chinese word (pronounced in the Cantonese way - actually several members of my family have similar sort of nicknames made up of 2 characters - one from the actual name and one other word)... so maybe... I dunno, LL could be... "Lam Lui" ? "Lui" means young girl in Cantonese.
But here's where I doubt this is the case for her.
Calling her "Lam Lui" makes little sense to me since it basically translates to "young girl Lam" and since she also has another sister, it seems silly to call Elisa that because her sister would be that too, technically... and 2 girls with the same nickname in the family just seems a bit silly lol
Without knowing her close family and friend circle, we can never verify if she ever had any sort of nickname that close ones call her by.
I'm inclined to just take this lead with a grain of salt for now..