Logically speaking, the old King Star should have passed the stargazing ability to the new King Star. However, she appeared to know nothing about it. It seemed that the former King Star did not wish for the incoming King Star to find out the truth about their change of power. He genuinely cared for her, which was something very unusual.
There was only one possibility. The old and new King Stars must be lovers, who swore to love as long as they both should live. The old King Star must be trying to avoid breaking her heart by not telling her the truth of his doom.
The old King Star would use any reasons, even with his betrayal, to cause them to split before his final days. He would break her heart entirely so she was no longer concerned about his existence.