I also think the are the same, for the reasons you two have already stated.
Recently, I had a new thought on why they might have changed the name back in PSI. The letters L and R, as you might be aware, are represented by the same character in Japanese and can be translated to English using either letter. That's why we have name differences like Palma and Parma in the games. I noticed that PSI and PSIV tend to use opposite translations. In PSI, we have Palma and Dezoris, in PSIV it's Parma and Dezolis, among other examples. I figure the same happened to Lutz. When working on PSI, the translators probably read it as "Rutz." Since it sounds a lot like
ruts, the mating season for deer, it would have caused a lot of problems if they used that name in a game back then.