Before Lu Shu arrived at the location where he sold stinky tofu, he had received distress points from Li Xianyi which led him to realize what an intelligent choice it was to leave Lu Xiaoyu with him.
Of course, he was unaware of the spoilt lightbulb. Lu Shu also reminded Lu Xiaoyu during breakfast to be careful not to leak anything about their powers even though the other party was a good person.
These days, it was impossible to see through a person's true nature without many years of interaction.
Swordplay was a separate matter and it should not lead to leaking your own secret to the other party.
If one day he and Lu Xiaoyu had to go into hiding, they would have to make sure no one could find any leads to them, then would it be considered safe.
Lu Shu had always been afraid of poverty and it would be practical to have some savings. The backup plan was his savings.