I looked around at some of the first impressions of Luminous Arc Infinity - there seem to be two camps of people. First, the usual group of people who like games with cute girls and passable gameplay (I'm guilty of this), saying there's nothing wrong with it and that it's fun. Second, fans of the Luminous Arc series who are furious that their beloved series got turned into some harem fanservice RPG.
I can sympathize with the second group, I'm sure I'd be furious too if I had a series that I loved and they suddenly turned it into something entirely different. I've never played a Luminous Arc game though, so I don't have to deal with the frustration they must feel. Many of them mentioned that the real successor to Luminous Arc in terms of gameplay and story was the excellent Stella Glow, which I played (and loved) a couple months ago. Of course, Stella Glow and Luminous Arc Infinity being on different consoles also probably stoked the fanbase fires a bit, too.
It's probably for the best that I'm completely ignorant of this series, and I can just go in hoping for good songs, cute characters and fun SRPG gameplay instead of having my expectations for a series shattered. My apologies to Luminous Arc fans.