This version makes much more sense than the other one, here Weiss revises his opinion from wanting a robe that's the best in the entire country to one that's the best in the entire world for his daughter. The other TL was the opposite and had him downgrade(!?) his ambition to protect his daughter.
Why would a loving parent scale back the protection they want to give their beloved child, especially since Lily's existence would surely be a matter of national importance? Heck, countries might even wage wars over her if they knew. So it makes sense for Weiss to want something for Lily that's better than anything offered in any country. Because she'll need it if their secret is ever revealed to the world.