This Lara Croft game (notice it's not called Tomb Raider) has of Lara Croft only the name. It's an obvious business savvy decision to limit the risks on this attempt at exploring XBLA and PSN on the part of Square Enix (Crystal Dynamics was bought a few years back). It could easily be a brand new IP with a new character, and I expect they very much used this game to explore new design ideas for a brand new IP they might be revealing in a while.
As a game, (I played the demo) it is a very solid action adventure title, quite a AAA one for the target platform and at a relative low price for its production values.