Current rumor is the 3DS Lite could be arriving around a Spring 2012 release date although it might just be in Japan. No 2nd stick would be built-in but the battery life would be improved by a lot and the system itself would be lighter.
The whole thing is just speculation and I assume the 2nd stick wouldn't be added because Capcom somehow has "exclusive rights" to the thing because they co-developed it and are selling it as a bundle with Resident Evil Revelations.
http://www.screwattack.com/news/3ds-lite-coming