They do a whole lot more than just kiss heheh
When the Summer Court Faerie King discovers his pregnancy took, he immediately joins Kayn to return to the Snow Moon Order. They had sent Kayn to kill him and he had failed, Ezreal doesn't trust the Snow Moon Order to let Kayn live after failing. Not to mention, the living breathing proof of an heir that can be an end to war and a beginning to peace. Lymere started this war, Ezreal had just been born into it. He was determined to make it right for his family.