Azalea is a temporary NPC and Lapis is in full control of her reproductive functions so she can choose to have a child or not. For the moment she chooses not to have one with the player as he hasn't proven himself worthy to her yet.
I'm working on Aria's pregnancy events right now. They will work a bit differently to how the system worked for Goblins. She will initially lay an Egg, and you will have the options to speed up its incubation. If no actions are taken to speed it up, it will hatch in ~20 Days. During this time, Aria will refuse to have another child with the player. Once the Egg hatches, her kid will run around the house and you will have options to interact with her to help raise her. After a few days of such interactions, the child will move out to live with Aria's parents in the village and will occasionally stop by to play outside Aria's home. If you take no actions to raise the child, it will never move out of her house and you will be unable to impregnate Aria until the child has moved out.