Does Lily approve of arranged marriage or not? I think that she knows that marriage is her duty. What do you think?
I think that your interpretation is correct. I do not think that Lily approves or disapproves of arranged marriage. She simply accepts it as the way things are. It is a part of her culture and her duty to be done to honor her family and ensure support for herself in life.
Early in the story Lily begins to undergo the foot binding process. Lily believes that she should stoically endure the pain of foot binding. She believes that if she can do that, then she should be able to endure her marriage and in-laws. Her attitude about a lot of cultural norms seems to be similar to her attitude toward the foot binding process and arranged marriage. Lily seems to apathetically accept the events in her life, because she knows each item is her duty to do as a woman. To do anything else would bring her and her family shame, which in many cases would be viewed as worse than death.