Lionhearth on Disk 2

[Bart's Friend Milhouse]

You don't need to read the Weapons Monthly magazines in order to upgrade your weapons. You just need the specific items required to remodel them in your inventory and enough Gil. The magazines just tell you what items are needed, nothing else.

I'm pretty sure (correct me if I'm wrong) you do need the magazines in order to upgrade your weapon. The choice of weapon to upgrade is triggered by your viewing of the magazine in the item menu screen just like the options to learn limit breaks. If you don't have the magazine then you won't be able to upgrade your weapon even if you do have the required items. However I have heard stories about acquiring Lioheart in disk one and given that the magazine displaying the prerequisite items is in disk three this conviniently suggests otherwise.
I'm also quite sure you don't need any of the magazines that display less powerful weapons in order to upgrade to your final weapon