The Jag STR has a 4.2 AJ engine. Not only is the LS a different size, but it's also unique to Ford. IIRC the closest Jag variant is a 4.0. They're all in the AJ family, but they're all a bit different. Trying to fit the Jag SC to the LS is like trying to fit Mustang 3v 4.6L parts to an Explorer/Vic 2v. Both are modular Ford engines, but they have different heads, intakes, etc, and aren't all that compatible.
The blocks are the same.