Get a long-running-process' output stream
Take a look at the me.raynes.conch library, it's a bit more versatile than clojure.java.shell. It's low-level API seems to be what you're looking for.
Not a detailed answer, but the source for Clojure's sh function is pretty short. If you reworked it slightly to remove the .waitFor (or added a higher-order function to consume the partial reads returned by the InputStreamReader as they arrived), you could probably get updated data as it's returned by the process. But be careful of deadlocks in case your subprocess expects input as well (as in your lein repl example).