For the first time, King Lucas approached Clementine by sending him a letter. Since he cannot leave the Lastoval Kingdom in the meantime, King Lucas expressed all the things he wants to tell in his letter and send it to his trusted people. When Clementine received the letter, he didn't give any reaction to it.
Just like Melissa, the young duke didn't send him a reply. But that doesn't stop the king from sending him more letters. King Lucas also apologized to Clementine because he was the one that cause Melissa's suffering. And on his last letter, King Lucas expressed his wishes to meet his niece.
Not only that, but the king is ready to give Melissa's daughter a royal title in their kingdom. It is only the right thing to do because her mother is a princess too. If Clementine will also permit it, King Lucas can also introduce him as a royal prince in their kingdom. It can also give them a good reputation and additional protection too.