Hm... well if you like the game, get the DLC. I mean Lost is complete after season 3 when they get off the island, but they still made 3 seasons after that. You could stop at season 3, but if you really like the show, I'd finish it.
Same with Alan Wake, the game ends on a cliffhanger, and if you're interested in the plot overall, get the DLC. It's very long compared to the game itself, and worth the price. It also sets the story up for Alan Wake 2.
It adds to the experience, and explains the ending of Alan Wake. I think it completes the game, but due to the noticably different gameplay, I can see why it's DLC.
Out of all the DLC I've ever gotten, this is probably the most required.