You can still get the Lionheart. You will need Tonberry to upgrade to it, though, since you can't enter any towns. Use his Call Shop ability to call a weapons shop.
There is a shop on board the Ragnarok. Plus I think Doom Train is the one that allows you to call a weapon shop; Tonberry just lets you buy items.

Also, I don’t really think you’ll need the best weapons or Eden to take on Ultimecia. Just run around the island closest to Hell/Heaven drawing Aura, boost your strength to max for a few characters (Flare with the Strength +60% ability should do it) and limit break the final bosses to death. Worked for me, at least.