As I didn't understand where to start a discussion, I ended up adding this franchise...
Anyway, in our close discussion where we decided to basically use normal case for the product names (e.g. Final Fantasy), "THE iDOLM@STER" was what was cited as an exception since this lower case "i" was seen to be intentional, but according to various websites, NBGI actually states
on one book this "i" is just stylistically used for the title logo and the official capitalization is "THE IDOLM@STER". I personally think some titles or companies looks better in all caps (e.g. SQUARE ENIX, but maybe it's just me), and am not really a big fan of "The Idolm@ster​" myself, so I'd go for "THE IDOLM@STER" from now on, but not sure what to do with
all these albums that have piled up with that lower case "i" over the past years.