The Source of Their Magic
I know Lulu and Lux are magical, but do rheir weapons enhance their magical abilities? Maybe the same could go for LeBlanc, but we don't much about her yet.
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It's an interesting question! I like to think that certain items are forged using magic, while others are simply a means for focusing the magic of the user.
I imagine a wand, for example, being like a conductor's baton - the baton itself does not direct the music, but it helps the conductor to do so.
Similarly, does a paint brush create art, or does the artist? Does a great, gifted artist need a super-special brush, or can they work with any?
However... if a great sorcerer forges a sword using magic, I'd expect that weapon to have magical effects even in the hands of a non-mage. :-)
Odds are most of their "weapons" are actually just focuses for it, as that's how it's most often handled in other games, books, shows, and movies.
If the staff were the ultimate source of Lux's power, Lux would not be a mage (and wouldn't be using it anyways, with how Demacia views magic), she'd be a girl with a magic stick.
For Lux, the staff is just a tool for it. A way to focus and bend the energies she couldn't if she didn't have it. It's like digging - you can dig without a shovel, but it's slow, hurts, and isn't as good, and eventually you hit ground too hard to dig in without one. But if you're using the shovel to dig, the shovel isn't the source of your digging, you are. The shovel is just the most efficient way for you to use your digging powers. Lux's staff is your metaphorical shovel.
For Lulu, Pix is clearly the primary source of her power (that, or the time she spent in the faerie world is, I dunno). The stick she uses is just a stick - remember, she's still basically a child in mind, and cool mages use staves, so she uses a staff because that's what her child mind comprehends. The staff might be used as a tool to direct certain magics (Glitterlance in particular comes from it, although we also see it come from Pix...), but the primary reason she uses it is just because her child mind is unable to comprehend that she doesn't need to use it.
Now, LeBlanc...She's a powerful mage in her own right, and we know this through lore. She may use the staff as a focus, but I'm pretty sure that the primary purpose of it is to hold that crystal in it. Odds are that crystal is a power source, although less in the sense that it makes her a mage, but more in the sense that it's a purple version of 
- It gives her more mana, basically.
It'd make sense for LeBlanc's R and passive to come specifically from her crystal mirror staff thing.
Brand bio:
"The Runes were the source of all magic in the world and, against his master’s warnings, he chose to seize that power for himself."
Make of that what you will