Well, let's say this. Every single weapon that your character has can turn into the Ultimate Weapon (for Lightning, it's Omega Weapon). Depending on which weapon you upgrade, the stats of the Ultimate Weapon will be different. Upgrading Gladius, for example, will make it Helter-Skelter, which can turn into Omega Weapon with a lot of strength. Upgrading Lionheart, on the other hand, will turn into Ultima Weapon (which is just a weapon, not an Ultimate), and if you turn THAT into Omega Weapon, you'll have the Quick Stagger ability, but less strength than the other Omega Weapon. To get any Ultimate, you have to upgrade a basic weapon, get it to Star Level, transform it, upgrade the new weapon to Star level, and then use a special transformation item, only available in Chapter 13, that costs 2,000,000 Gil (which took me hours to get). So don't plan on getting it soon.
sig credit goes to Craizen
Resurrection in process:
Final Fantasy Eternal