The bloodline of Gawain and Guinevere began when Guinevere caught Gawain's fire tear. A result she absorbed some of the fire but not all and became part dragon. She gained new abilities like her eyes could go to violet the other is very important. She could reproduce without the need of a human father. If she kilned an egg she would get a daughter or the very small chance of a son. Gwendolen touched the fire as well so she could reproduce as well. The known bloodline of Gawain and Guinevere starts with Gwain to Guinever and many generations after to Liz and Lucy is the youngest dragon princess. 

It can be arguable that the clay dragons are Gawain's children since they have his fire tear auma. Grockle can also be called his son because while in the barn with Brother Bernard he asks who his mother and father are and he said Zanna and Gawain.