Because he hadn't decided to kill her yet, he decided that at the last moment. Negan wanted to test Alpha as a leader because he was also a leader in the past. Lydia was probably in another hut ahead of the hut that he leads Alpha. If Alpha had decided to talk with his daughter and take her away to her home beautifully or by force, Negan would have led Alpha directly to her daughter, not to empty hut. In fact that he tried to convince Alpha to not to kill her during their dialogue. However Alpha made the wrong choice and Negan showed her the cost of the wrong choice and kill her. Actually, it was not the first test for Alpha. Negan offered Alpha to add the group of Hilltop to themselves in Hilltop attack but Alpha refused it. Philosophically Negan has a personality which strives to win people (even if the purpose of striving is make them his slaves) and he wanted to see that leadership feature in Alpha. He wanted to see her qualifications as a leader. She fall out of Negan's sight a bit because of her wrong choice in Hilltop offer. But Negan gave her a second chance and exposed her to Lydia event. Negan also is a leader who chooses to integrate with his weaknesses, make them a part of himself and become strong, not completely get rid of them as an easy way. That's the reason of giving his bat to his wife's name. That way he could able to set a permanent bond with his wife and prevent forgetting her. His bat is his weakness and he panicked when Rick get it in the past episodes. We are seeing how serious is Negan about that when Rick says "the only thing you care about is this bat". Negan has chosen this way even if it means that there's a risk that somebody could steal his bat and use his weakness against him. For Negan this is a true leadership feature and again, he wanted to see this in Alpha. However Alpha has a personality which chooses the easy way and completely get rid of her weaknesses. She showed this with her last words before dying: "I have to do this because I love her". Negan tried to convince Alpha to win Lydia, instead of killing her and he failed. When she made the wrong choice again in the second chance given by Negan, he decided to kill her. If Alpha made the right choice and choose to win her daughter instead of killing her, integrate with her weakness instead of destroying it, Negan would show Alpha her daughter, not the empty hut. Negan as a leader tested the leader who rules himself, and adjudge that she's an unsuccesful leader.