Princess Kate had an “emotional” lunch with King Charles before recording her heartbreaking video, sources have claimed. The King, who also has cancer, travelled from London for a private lunch with his “beloved daughter-in-law” Kate on Thursday. The Princess of Wales, 42, was keen to speak to Charles and find out how he was coping. It is thought the pair talked about Kate’s video announcement in which she said the discovery was a “huge shock” but vowed she was “going to be OK”. A source said: “It is highly unusual for just the two of them to sit down together like this. “The King had already …