Does Sivir Legend become ready when enemy unit dies on opponent's turn?

Yes, Sivir's Legend ability will trigger and ready her if an enemy unit dies during your opponent's turn.

According to the card text for Sivir (Battle Mistress), her ability states: "When one or more enemy units die, ready me."

As established in the related FAQs, triggered abilities like Sivir's are active and can trigger during the opponent's turn whenever the specified condition is met. Since the condition is simply "when one or more enemy units die," it does not restrict the timing to only your own turn.