There's no lite version yet, but last year MLB released a free version sans audio and video, so if you just want the scores, you can wait and see when that one shows up.
Meanwhile, if you want official baseball info beamed straight to your phone all year long, this app is the way to go. While there are definitely lots of other apps that will hook you up with scores and alerts for a much cheaper price, the MLB app is a quality way to get information straight from the league. Especially if you're going to be following baseball closely all year, the $15, while steep for an iPhone app, is definitely worth it. Personally, I can't wait for this season to start. Play ball!