@Kaarme You haven't spent much time around 15 year olds have you? And time spent when you were a teenager doesn't count. Most of them certainly aren't mean spirited but they look at the world through a narrow lens and rarely ever try to think about things from someone else's perspective. That's not to say that they won't help if a friend or even an acquaintance asks for it, but in normal situations, 9 times out of 10, they're only thinking about themselves. That's called being selfish. Learning to broaden their perspective and think about other people is part of what becoming an adult is about, and they've only just started that.
As for Lefiya controlling Ais's social circle, show me an instance of Lefiya trying to get rid of someone other than Bell and I'll give your theory some credence. Until then it falls under the category of just not liking Bell. In fact show me an instance where she has tried to get rid of Bell. Also Ais and Lefiya have the same social circle. The only friend of Ais that Lefiya doesn't share is Bell and the only friend of Lefiya that Ais doesn't share is Filvis. Therefore when someone new is brought to the group Lefiya has every right to say "No, I don't like this person. I don't want them here." just like Ais, Tiona and Tione have the right to say "I do like this person. I do want them here." Friendship is a democracy man, not a dictatorship. In fact, unless you have no friends, I'd bet that you have experienced something like this in your real life. Someone brings a new person and the group splits into 3 factions, "I want them," "I don't want them" and "I don't care." Then you effectively vote, though it's probably not that formal.
For why Lefiya doesn't like Bell you've got part of it, but only part. Remember Bell made a remarkably bad first impression with her. Intentionally or not he made a fool out of her, then she saw him and her idol "cuddling." Then throw on Lefiya's jealousy over Bell spending time alone with Ais. Finally add on the facts that Bell is beginning to trigger her inferiority complex and the fact that she hates to lose and frankly I'd be astonished if she didn't dislike him.
Also speaking of first impressions did you start Sword with the novel, the manga or that travesty of an anime?