Lucan and Sarina spent a lot of time together, and they had a threesome with Katie, and even went on a trip, just Sarina and him. They enjoyed a lot, doing all sorts of things, and at one point they even decided to have a baby but they decided to hold it until Leira became 18 years old. Until then no baby.
At this time, Lucan also thought that it would be better o have only daughter, since he had relationship with his mother, he knew that incest might spread to his children, so if he had son and daughter then incest would be bad for them, and he doesn't want that to happen with them. After all, at one point he had to tell or they will figure it out themselves that Lucan, Sally and Eloise were siblings. This might simulate then for incest. Lucan incest were only with Sally and Eloise, he would never have any other incest, like his mother or his daughters.