In that situation, Terror will not help you prevent the opponent from winning.
As you noted in your own answer, drawing a card during the draw step does not use the stack and thus cannot be responded to:
504 Draw Step
504.1. First, the active player draws a card. This turn-based action doesn’t use the stack.
Laboratory Maniac's ability creates a replacement effect. If you cant respond to the replaced event (card draw), you also can't respond to the replaced event (game win for your opponent), because the replacement effect happens exactly when the original effect would have happened.
Even if Lab Maniac's ability was a triggered ability (which is purely hypothetical because in that case it wouldn't work as intended, the controller of Lab Maniac would lose before winning the game), Terror still wouldn't help you because the Maniac's ability would already be on the stack and resolve eventually.
Your only chance to prevent the loss is to have Terror resolve before your opponent draws from an empty library. The Upkeep step happens before the Draw step, so that is the last opportunity to kill the Lab Maniac with spells or abilities.
As for Scenario 2, if the card draw is the result of Staff of Nin or any other spell or ability that uses the stack, you can react normally with Terror and prevent the Maniac's replacement effect by destroying him before the draw could even be replaced. Again, if a replacement effect happens, it happens at exactly the time when the original effect would. If the original effect never happens, then neither does the replacement:
614.7. If a replacement effect would replace an event, but that event never happens, the replacement effect simply doesn’t do anything.