Ayumu's pretty competent with wakizashi/short swords but she tends to use them more as back up weapons than primary ones. Ninjutsu swordplay involves a lot of stabbing maneuvers rather than slashing ones so while she could probably train her to have a solid base, the fighting style would be more precise and evasive than what a samurai might do. In general, Ayumu's sword style is more hit-and-run with escape in mind rather than one involving extended fighting. Ninjutsu style is generally designed to silently and swiftly disable opponents so I'm not sure if that's what you're looking for but Ayumu would definitely be willing to teach Lux what she can!

Ayumu might offer to teach her some observation/prevention tricks to keep her Victorian shounen in line, too. She's very versed with pressure points that numb the body if that's something Lux might find useful! (In her experience, it's harder for boys to get into trouble if their limbs aren't functioning well enough to carry them into it.)