I had them together for over three years. My male Lyretail mostly ignored the Purple Queens, but my male Purple Queen actually defended himself when the Lyretail would try to chase him. IMO the two problems to over come are a large enough tank so there is plenty of room for the Purples to shoal away from the Lyretails and more importantly getting enough food to them multiple times a day because the Lyretails are the more aggressive eaters. I used a separate acclimation tank for the Purples so they were all healthy and eating well before they were added to the DT. I also had other peaceful Anthias in my DT at that time like Dispars and Ignitus. They would actually all shoal together away from the Lyretails.