This is actually occurring. Most advances are made in cross-platform libraries (networking, regexps, threading, pattern matching, lazy evaluation, etc.) but some implementations have their own extra that make them interesting (by no means an exhaustive list):
ABCL (http://common-lisp.net/project/armedbear/) runs on the JVM.
CCL (http://www.clozure.com/clozurecl.html) has excellent integration with Objective-C and Cocoa on OS X.
ECL (http://ecls.sourceforge.net/) is easily embeddable in C / C++.
The commercial offerings Allegro CL (http://www.franz.com/products/allegrocl/) and LispWorks (http://www.lispworks.com/) keep on improving and extending their own implementations in interesting ways.