Really if you boil Litchi's character down she's not a very good person. She's extremely selfish, guilt driven, and makes lots of choices that ends up being worst than the addressing the problem directly.
Even her trying to save Ara can be considered a selfish act because she's in the same boat as him and she feels if she doesn't save him she can't save herself and then maybe, just maybe, she'll be able to forgive herself for how she treated Lotte.
She puts on the nice girl act simply to make herself feel better, not because she's a good person. And most of the time those people she helped were simply because they had some connection with Arakune and by associating with them the chances she could run into him.
And since the NOL have Ara now, it's a no brainer that she'd join up so she can be closer with Ara and will probably do anything she's asked because of that.
Litchi is far from being considered a goddess.