Lightning and her sword has not yet been released, but we are given some intel on her weapon from the news. Basically, her weapon, similar to many collab weapons such as terra and celes' weapons, has a dungeon that you can farm recipes and mats from. However, different from those, there are two versions of the weapon available.

If you craft the weapon from the ground up with recipes like normal weapons to lvl 5, you get the following weapon passives: 15% slash and missile dmg up, 15 acc. These weapons can come in assault aim and vital variants. (stats are not disclosed yet)

However, you can also acquire pre-crafted versions of this weapon from mission rewards. this version has instead the passive of: 30% undead/machine killer, 15 acc, and only come in the crit variant. You can get 1 3 from the hard quest 1 4 and 1 3 from the vhard quest and 1 5 from the nightmare version of the quest. meaning that you can get 2 5 versions of this type.

Both versions get a Lightning(the unit) exclusive effect of 30% thunder dmg up and 30% reaction block rate. Making it extremely powerful and a complete upgrade from coral sword(which is also getting 6 next update) for lightning.