"On account of this personal union, which cannot be thought of nor exist without such a true communion of the natures, not the mere human nature, whose property it is to suffer and die, has suffered for the sins of the world, but the Son of God Himself truly suffered, however, according to the assumed human nature, and (in accordance with our simple Christian faith) [as our Apostles' Creed testifies] truly died,
although the divine nature can neither suffer nor die. This Dr. Luther has fully explained in his Large Confession concerning the Holy Supper in opposition to the blasphemous alloeosis of Zwingli, who taught that one nature should be taken and understood for the other, which Dr. Luther committed, as a devil’s mask, to the abyss of hell." Source:
VIII. The Person of Christ
Luther's Works, volume 41. “We Christians should know that if God is not in the scale to give it weight, we, on our side, sink to the ground. I mean it this way: if it cannot be said that God died for us, but only a man, we are lost; but if God’s death and a dead God lie in the balance, his side goes down and ours goes up like a light and empty scale. Yet he can also readily go up again, or leap out of the scale! But he could not sit on the scale unless he had become a man like us, so that it could be called God’s dying, God’s martyrdom, God’s blood, and God’s death.
For God in his own nature cannot die; but now that God and man are united in one person, it is called God’s death when the man dies who is one substance or one person with God” (LW 41:103–4). Source:
What Luther Says about the Death of God