When I ran CL server (it was in-house service, but heavily accessed 24/7 and I couldn't stop it to update frequently), I used a few ways, depending on how imminent the problem was.
The normal routine was to change the source, test it, then from server REPL I just reload it. If the problem was more serious that I had to fix it ASAP, I sent the definitions directly from the editing source to the REPL (in Emacs it's just a couple of keystrokes).
It was only when the situation was extremely serious (e.g some bug stopped large part of the production pipeline) that I typed expressions directly into REPL and afterwards I put the fix into the source. It was pretty rare, though.