once the Garden becomes mobile under your control on disc 2 it is fairly simple to get the Lionheart. you can Dragon Fangs from Blue Dragons near Trabia Garden and you can steal Power Generators, which refine into 20 pulse ammo each, from Blitz enemies near the Centra Ruins and those are the only difficult items to find.

I usually get the Lionheart asap once the garden is mobile just so I dont have to worry about upgrading later on