I don't know why, but I find Lux-Pain absolutely horrid. I like the premise - the idea the story is based upon is intriguing and the overall presentation looks nice... but... the gameplay... I really tried hard to give this game a chance, I "started playing it" three times already and I just... can't. Maybe it's because the game has a hard time explaining itself, maybe it's the pseudo-exploration, maybe it's the cryptic goal of the game, but whenever I reach the school in-game and find the first few WORM's, I just shut off.
I can recommend Time Hollow - the game was amazing. Same goes to Trace Memory/Another Code (however that's a slightly different type of game), Last Window and Again. 999 is pretty amazing, but it's more of a visual novel. Touch Detective games are a "different kind of mystery", but they're quite entertaining as well. Ghost Trick mixes the point-and-click adventure style with a healthy dose of a puzzle, if that's your kind of thing - I found it very enjoyable. There's also a port of the ever-amazing Broken Sword: Shadow of the Templars, however you're better off playing it on a bigger screen to fully enjoy it. That said, it is an option. Last but not least, there's the under-appreciated Metropolis Crimes which I cannot recommend strongly enough - I don't know why this game didn't go huge.
Games from the "mystery" genre are actually quite numerous on the DS, it's just that it's hard to find really, really good ones among them. It's mostly shovelware of the likes of the CSI games. There's also Crime Scene - it's considered shovelware, but I suppose you could squeeze a dose of fun from it if you overlook its limitations...
If you're in the mood to try "something else", I also recommend Trauma Center games - fair enough, they're not much of a detective story, but they're an interactive adventure none the less and they're worth playing.
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Additionally, the DS has its own port of SCUMM VM, if you're interested in some old-school adventures.
All in all, the DS is a real gold mine as far as those games are concerned, mainly bacause of its touch screen.