Although Luke was full of uncertainty about how Oukiwa would be during his absence, the consent of Ayumi Yamazaki was the primary point for him actually to make a decision.
He knew that there was a possibility that the First Servant was very angry after the terrorist attack had failed, and that when he became Champion of the Tournament of Legends, the Big Demon also knew where the half-wolf might be, but it would be too risky a move to attack the Strogueher.
What is the largest Noble Family present in Oukiwa is not only very influential but also very strong, not to mention their powerful guards, who are very experienced and come from many parts of the Empire. Not to mention that the Strogueher property is, after the Central Palace, the best-guarded area in the entire city.
Knowing all these factors precisely because he had lived in this place for almost three weeks, Luke was somewhat reassured.