They can't fight unless Ionian allows Noxus to have a re-rematch. Rematches are only supposed to happen every 15 years, and Noxus could have just allowed that to happen instead of having the rematch 8 years after the initial match, but Noxus was under sever public relations preasure due to the massive sympathy Ionia gained by the various protests against Noxus holding their lands. They risked war with Demacia if they didn't have that rematch.
Ionia does not have that same pressure. It wouldn't make sense for them to fight Noxus again unless they are colossal idiots who want to be invaded.
Unless you just mean another event in the same theme as Ionia vs Noxus, in which case, yeah that would be cool.