buildinva, probably it will fit, in the broader sense of whether the bolt spacing is the same and there are sufficient support points on the toilet bowl to keep the seat from wobbling. The main issue would be the amount of clearance behind the bolt attachment points and in front of the toilet's tank: the Inax Luscence has its own tank for heated water in that area, and the toilet seat hinge, accommodating the seat's tank, might lack sufficient clearance to allow the seat to swing all the way up.

Aside from the mechanical issues, however, the Inax seat is squared off at the rear, where the AS toilet tapers in as it gets nearer the toilet tank. You are going to have an overhang on the sides at the rear of the sat that may clash with the lines of both the seat and the toilet.

A Toto Vespin II has similar styling to the AS toilet you linked, and (from personal experience) I can tell you that it works perfectly with an Inax toilet seat (ours is a Clessence, not a Luscence). Of course, the Toto is a bit pricier than the AS, and is not sold a Lowe's.

Here is a link that might be useful: One Vespin II installation