Death is truly a mystery that burdens all of us, even believers. However, there are glimmers of light that can begin to dispel the darkness.
First, death is part and parcel of material beings. Since we have bodies, our bodies are naturally subject to break apart. So, one can argue that death is natural given the nature of human beings and the material world we live in.
It’s important to note that this doesn’t count against God since he was perfectly free to create any type of world he desired. He was not bound by any obligation to create a world with a certain amount of goodness—only goodness that is consonant with his Divine Nature.
Concerning the question of God deciding who dies, death experienced by material things does fall under God’s causality since He is the sustainer of all being. There is no life that comes into existence or goes out of existence that is outside his causal power. Concerning humans, he determines when our lives begin, he sustains our lives right here and right now, and he determines (most often through secondary causes) when we will die.
We can rest assure, however, that God does not allow any evil, especially the evil of death, without willing a greater good to come from it (see Rm 8:28).
With that said, according to paragraph of the Catechism of the Catholic Church, we know that if Adam would never have sinned then death and suffering would never have entered into human history. Out of pure generosity, God planned to preserve humans from death had Adam obeyed. However, Adam forfeited this gift through his sin. As such, all of Adam’s progeny must suffer the natural ordination of our nature—namely death.
But there is hope for restoration. God did not leave us orphan. According to Christian teaching (see Jn 5 and 1Corinthians 15), there will be a bodily resurrection where all souls will be reunited to their bodies and death will be no more. God will restore what Adam destroyed. All suffering will be redeemed.
Obviously these brief comments can’t totally dispel the mystery of God’s permission of suffering and death. But a little light goes a long way in the darkness of mystery and can provide hope in the midst of suffering.