Also of course the default is to not get the debugger but let the server thread crash and print the backtrace. With a user setting, you can choose to get the debugger, and have this request wait (the connection may time out, which isn't an issue during development). Another setting is to print the backtrace in the browser (= dev mode).
Now, if your entire server is taken down because one connection threw an exception, that's bad design. But pretty much no major language works that way. All of them allow you to set things up so that an exception handling connection A won't affect connection B. And if you've done that in Common Lisp, then connection A halting and waiting for the debugger won't affect connection B either.
Anyway it sounds like this isn't really the target use case for the debugger since restarting a webserver is supposed to be easy. Maybe there's a different use case in mind?