What does LI means? Love Interest?
Yes, correct. LI = love interest.
guess time for me to replay the game well after the update drops. Seems I dont recall as much as I thought I did as I thought they the reason they were wanting to "teach her a lesson" was something on the lines she knows to much after helping Emma ( the model) in the past think that was her name. Also seeing how she was getting close Kaylah to not go below deck and staying close to her for most of yacht party. It might of seem like she was talking and saying to much since they never properly dealt with her last time since she is still alive. But I'm starting to think the majority of this might be more of my interpretation and I just forgot chunks of the story since you said the villain's never really gave a real reason for doing things.
We're told during the latest investigation discussion Agent Fox that is, at least in part, one possible motive for that. Emma (you had the name correct) had talked with Charlotte about what was going on. Emma decided to go to the police, but since they were corrupted she was killed because she said she had evidence she could use against the criminals. (Either the corrupt police took it upon themselves to silence her or they were told to by higher-ups.) They apparently also think Charlotte might have evidence because she had spoken with Emma. They believe Emma gave Charlotte a copy of the tape (or whatever it was) incriminating some from the organization.
So, however much of that matches up with what you were thinking, it sounds like you were remembering it pretty much. And yes, they weren't happy with her at the yacht party, but I don't think that single instance (even if it were just a single girl being protected over and over) would've been enough reason to act. Wolfe seems unhinged, but his bosses probably have curtailed some degree of what he wanted to do.