In keeping with her mission from Queen Brahne of tracking down Princess Garnet's pendant, she will always attack Dagger if she is conscious. In keeping with her other objective of killing Vivi, she will attack him if Dagger is KO'd. While she will normally continue to attack Dagger, Lani will sometimes switch and briefly focus on another character when they come out of Trance or attack her physically.
Her high Speed and use of level 2 Black Magic make her a force to be reckoned with, particularly if the player party is at lower levels. She will sometimes rant at the player while counter-attacking a physical attack, yelling, "What do you think you're doing!?"
Zidane should steal all of her items, and when he's done he should start attacking. Vivi should use his Black Magic to hurt Lani (Bio is effective). Dagger should heal herself and her allies, and Quina should attack or use Frog Drop if s/he has caught a lot of frogs. Casting Reflect on Dagger makes the battle easier. As Lani is a humanoid, equipping Zidane with the Man Eater is recommended to increase his damage output.
An effective strategy to neutralize Lani is to equip Dagger with Chemist and Auto-Potion and have her repeatedly cast Reflect on herself. Quina should cast Magic Hammer to deplete Lani's MP until she can no longer use her spells, then cast Vanish on Dagger.
A combination of Dagger's Blind, Vivi's Slow, and repeated uses of Quina's Magic Hammer and Vanish, will render Lani almost entirely ineffectual. If Dagger is equipped with Chemist and Auto-Potion it will allow for virtually unlimited steal attempts.
By far the fastest and easiest way of winning the fight is bringing Quina into the fight with 1 HP, easily done with Quina's Auto-Life spell, and casting Limit Glove on Lani. This will deal fixed 9999 damage to her, almost double her Max HP.