While it's awesome to make yet another Lisp, I think it's far more awesome to have a well-defined Lisp that can run on multiple places.
But it wouldn't. A Lisp that ran on the JVM would be able to use JVM libraries, one that ran on .NET would be able to use .NET libraries, one that ran on Rubinious would be able to use Ruby libraries.
Sure, the core Lisp language might be the same, but as soon as you started doing real work connecting it to outside code/services/devices etc, it'd rapidly become non-portable.
That doesn't mean it would be useless: being able to think in one language over multiple platforms would reduce cognitive load for developers.
(That said I realize you were looking for a Common Lisp, but sometimes good enough is good enough ;) )