Once you clear enough battles you are permitted to climb to the next floor of the tower, but doing so requires you to perma-kill one of your party members. The killed character will transform into an accessory that will grant another character their psychic powers, but that item won't learn any new powers, keeping you from using their unlearned abilities for the rest of the game. This seems like hard decision... until you're told there is a traitor in your midst. Obviously it seems like the game wants you perma-kill the traitor.
To figure out who the traitor is you have to use them in battle. At every battle's completion, you will hear your party members' thoughts but you won't know which ones are coming from which character. 3 characters will have "suspicious thoughts" and one of those three characters is the traitor. You can then use vision points, which you earn after important story battles, to read a character's mind and figure out if they are the traitor or not with complete certainty. You don't have enough vision points to check every character, so you have to alter your battle parties up, like you are playing a game of password, in order to find exactly who the suspicious thoughts are coming from in the hopes of spending as few vision points as possible.
But you don't just get to choose who to kill. Everyone has to vote on it. So out of battle you have to spend time talking with other characters and becoming friends with them so they believe you when you point at someone and call them a traitor. Using someone in battle also raises their friendship level, but you'll be using the traitor a lot just to figure out who they are. It's a complicated web of paranoia and trust that is a lot of fun to unweave.
The game starts to unravel when you reach the next level and you have to find the identity of yet another traitor that couldn't be detected in the level before because... reasons. You do this over and over again until you realize that eliminating traitors wasn't even the point! It just makes the second to last battle easier. Instead, you have to raise your friendship with everyone to maximum in order to unlock the true ending. Now you have to start a new game+ just to make friends with everyone you didn't make friends with before.
Except now the traitors different! If someone you are trying to make friends with ends up being a traitor early on, you are screwed! You either A) let them survive so that the end game is harder, or B) kill them and play through to the end just for the chance to select new game + again, hoping that your random traitors come out differently this time. Neither is a particularly appealing option.
This is what I meant when I said the game didn't make sense to its own developers. It feels like they weren't sure what they wanted your goal to be, finding traitors or making friends, because these goals interfere with each other. A single play through of Lost Dimension, where you try to root out traitors and trick out an awesome psychic battle party, is a lot of fun. But the things you have to do to reach the true ending are tedious and random. The normal ending is very unsatisfying, but the true ending is so random and unexplained it's also unsatisfying. So I suggest you ignore the plot and appreciate Lost Dimension for its deep battle systems and interesting traitor mechanic. I would certainly say that Lost Dimension is a great game, but the game is the only part that's great.
Bottom Line: Lost Dimension is a fun and deep tactics RPG with interesting mechanics and a horrible story with horrible endings.
Recommendation: Strategy gamers, war gamers, and anyone else who likes to crunch numbers will love Lost Dimension, provided that they don't care much about plot.