I've always wondered this and watched many many games trying to see it happen, but I've yet to see evidence of it.
Does the lumberjack do anything special if it meets an opponent's log mid-roll? Is he supposed to? The flavor text on the lumberjack card seems to indicate that it does, and it would certainly make sense. It says "He chops trees by day and hunts The Log by night." The Log is even capitalized as if to refer specifically to the legendary card The Log.
However, I've never seen any evidence that it does. When the lumberjack first came out, it seemed like the only reason to even use him, aside from the rage effect when he dies.