Can I trigger Zhonya's if a unit dies at another battlefield?

Yes. Zhonya's Hourglass saves a friendly unit regardless of which battlefield it dies at.

Zhonya's says "If a friendly unit would die" — no battlefield restriction. Since it's a replacement effect (not a play ability that targets), it applies to any friendly unit anywhere on the board, whether the unit is at your base, at a different battlefield, or even in combat elsewhere. The battlefield where Zhonya's is placed only matters for where it sits, not for the range of its effect.