Are there any Common Lisp implementations for .Net?

If it's OK to go the other way around, you can access .Net from your favourite Lisp through Edi Weitz' RDNZL.

Reconsidering this question from 2008 in 2010, you now might want to consider Clojure on the CLR. It's not Common Lisp, but it will be fairly easy to learn if you are coming from that direction. Interoperating with the CLR is dead-easy, it takes on more users every day and addresses several other important topics like concurrency. Might be worth investing some time in it. More CLR specific Clojure info here.

I haven't looked at it recently, but at least in the past there were some problems with fully implementing common lisp on the CLR, and I'd be a little surprised if this has changed. The issues come up with things like the handling of floats where .net/clr has a way to do it that is a) subtly incorrect b) disagrees with the ANSI standard for common lisp but c) doesn't allow any way around this. There are other similar problems. This stuff is fiddly and perhaps not too important, but means you are unlikely to see an ANSI CL on the CLR.

There are bigger issues, for example common lisp has a more powerful object system, so you can't map it 1:1 to object in the runtime (no MI, for one). This is ok, but leaves you with an inside/outside sort of approach which is what a common runtime tries to avoid...

Whether or not you'll see a common lisp-ish variant running on it is a different story, but I don't know of any at the moment (not that I've looked hard)

No, but you might want to consider IronScheme running on the DLR.

From the website:

IronScheme will aim to be a R6RS conforming Scheme implementation based on the Microsoft DLR.

IronScheme will be a complete rewrite of IronLisp incorporating lessons learnt while developing IronLisp.