There's a difference between diminutives and nicknames, imo.
For example, "Robert" may be called by diminutives such as Rob, Bob, Bobby, Bert etc
His nickname, however, may be Pudding Head or something because his friends remember an unfortunate haircut he once had.
I remember a thread here where someone wanted to call their son something - I can't remember; say, Thomas, use a diminutive say, Tommy but wanted his nickname to be Ace.
I wonder how far Tommy got with telling people he was called "Ace" really.
Someone I knew told me her nickname was "the Snow Queen" because she was beautiful and also not easy to get into bed. An acquaintance of hers said she was actually known as the School Bike.
I just called her by her given name.
"Lolo" is apparently already called that by her bestie.
So she's got a nickname.
Good.
If she wants her other friends to call her that, she should tell them.
Of course, the other friends may cheerfully tell "Lolo" to get over herself and give her a nickname like Pretentious Pants. That's how nicknames work.
Eta My name here is LaMarschallin, sometimes gets shortened to LaMar, but I'd like you all to call me by my nickname of BeautifulWonderfulPoster.