LCCS is written in ActionScript 3 (and Flex MX components, unless you use the Flash-only version) so I don't think it would work in FlashLite.
I know that the latest FlashLite supports a subset of ActionScript 3 (the original one was definitevly AS 2) but I don't know if it would be enough to run LCCS (my feeling is not, but you can try one of the sample apps)