However, "You sing, which I didn't know" just implies that {lo nu ...} in the beginning was dropped. But NOI states that there is a terminator of that {lo nu}.
The can only allow dropping articles when it doesn't lead to ambiguity like{broda cu brode} definitely means {lo broda ku brode} and{do sanga noi mi na pu djuno} means {co'e lo du'u do sanga ku noi mi na pu djuno ke'a}.