So I just figured out why L!Lucina uses a bow (like 3-4 months late)

I never that's why Lucina used Thöng. Never played Warriors. :)

I think it's simply because she can reclass to Archer, but Warriors isn't the only other spinoff that has Lucina wield a bow. In Project X Zone 2, she has attacks involving her transforming into the Bride class and using legendary bows and lances for weapons.

She also shoots mini Geirskogul's