The Princess in the Tower is a side quest in Dying Light 2, at the end of which you have to make another choice. You can lie about Timur or tell the truth. Let's talk about what both solutions will lead to.
The task itself is performed at night, and it begins with a conversation with Rose, who is standing on the balcony of the building. She will tell you that her brother locked her here. She wants you to find Timur, her lover, and ask him to save the girl. When you take the task, you will have the opportunity to rewind time to the night. If you don't make it, go to bed.
Go to the building with the infected, sneak past and collect resources. Find the door, but before you knock on it, you will run into Rose's brother. He will say that Timur is outside the door. Once you figure out what's going on, you'll have a choice: lie or tell Rose the truth about Timur.
If you lie and say that Timur is not here, Lowen will thank you and leave to tell Rose the truth. The quest will end and you will receive 750 combat experience and 150 coins. If you decide to tell the truth, Lowen will be upset, but the quest will end anyway and you will receive the same rewards.