I do believe that Lily had the right to cancel. I think there are many ways her situation could have been approached.
For the question, "How do I…not get the client upset." A solution was provided. One solution of many available ways to go about handling her situation. As with anything, a person can agree and say yeah that makes sense, or a person can disagree and say say ok thanks for the input but I'm not going to handle my situation that way. To each their own, options presented can be accepted or declined. Easy. However…
If the date was going to be cancelled no matter what, that's different. It would have been nice to have had that clarification added in at some point.
With the comments made, I couldn't tell if she was planning to cancel the date no matter what because of her own personal reasons or if she was willing to follow through with the date had the client still wanted to see her.