If I'm not mistaken, you have to play one O-Ring, target the other artifact, and THEN play the second, otherwise the first one would end up removing itself as the only legal target. Also, when you sac Lion's Eye Diamond, you'd have to discard your hand instantly (it got an errata to work as an instant, NOT as a mana ability), so you wouldn't have O-Rings to play. Unfortunately, it doesn't work the way it is.
PS: There are easier way to cause a draw...