How does his physical body not exist? It definitely does- that's how Lille's clothes don't fall off. That's how Lille can still stand on ground. Lille is still
there. What X-Axis does is that it makes an incoming attack "penetrate through" him instead of actually hurting hi, it's similar concept to his shots:
Shikai Hyoketsu is not some kind of "attack" that Toshiro is throwing at Lille. Shikai Hyoketsu functions by simply freezing all matter before him down to the fundamental Reishi instantly. It's not a wave of ice, it's not a slash, it's not an ice blast.
Lille's physical body exists as a matter before Toshiro, so it would get frozen. There's no attack for him to just "phase through", Toshiro is not
throwing ice at him, he's straight up freezing his body and the fundamental Reishi that it is made of. He's directly affecting the composition of Lille's body rather than attacking it.