Tomb Raider: Legend uses a custom made engine. Or should I say engines, because they're technically custom made for each platform. We have a generalized rendering interface and a scene-management/culling system, but the next-gen PC path is the only one utilizing it - the engines for PC prevgen and all the other platforms (except for the handhelds, I don't know anything about them) were manually handcrafted, so to say. I wouldn't even call it an engine, it's too down to earth for that.
While this isn't a very efficient approach in terms of labour, it very much was in terms of performance. It does what it has to do and nothing else, so it can be completely optimized for the game and the platform. However, this isn't the long-term approach we're heading as I'm currently porting our general next-gen engine from PC to Xbox360 (a quite joyful experience I might add, it's a great platform to develop for - but that's a previous PC fanboy talking, haven't got any experience on any of the other consoles ).
As for the yankee part, the game was indeed developed by Crystal Dynamics (Menlo Park, California). But the company has a long history with the Dutch Nixxes Software BV (where I work), which originally had porting of games as it's core business. But nowadays we're more like a co-developer, focussing on both tech and tools.