Does dua change what is written in al-Lawh al-Mahfouz?

No, because what is written in al-Lawh al-Mahfouz can never change. Rather, what changes is the Qadr of Allah as mentioned in authentic hadiths. What that means is that Allah knew from the beginning that the person would make dua asking Allah to repel any evil that He may have decreed for him, and Allah had also written that change in al-Lawh al-Mahfouz. Hence, it is all within Allah’s Qadr.

For example, consider a sick person taking medicine. It changes his ill condition to a healthier one. Both the sickness and the taking of the medicine was part of the Qadr of Allah.

And Allah knows best.