Lost Via Domus is based off the hit tv show Lost. It does what it has to do. But all in all this game is a fan service.
You play as a brand new character added into the doom flight 815. His name is Elliott Maslow. Once you crash on the island Elliott loses all his memories. So thoughout the game you have these flashbacks, which is an big element of the television show. And in these flashbacks we as the gamer learn about Elliott's past. And Elliott himself is learning about his past. So it was a smart thing to do for the developers to incorporate this into the game.
The game is fairly short. I completed it in 6 hours. It was also in one sitting.
Would I recommend this game? Yes and No. Yes for the fans, but to rent it out from your local video store. No for people who have never watched the show. This game won't be remembered as a great game because it isn't. It will be remembered among Xbox 360 gamers as a easy achievement game. Which is sad.