I think to trigger the lightsabre training you have to have:
1. Visas equipped with a lightsabre
2. One single blade lightsabre equipped on your PC
3. A spare single blade lightsabre in the GUI equipment screen.
Plus it does absolutely nothing for you that I've found so far. No XP, no new features. Just a device to measure your single handed, double handed and unarmed fighting capabilities against a common foe comparatively.
I would actually back a mod which gave you something like awarded the next tier of two-weapon fighting unless you're already maxed out, for defeating Visas in all three duels.
To trigger it you might have to unequip your second PC lightsabre and leave it in the GUI equipment.