if something is on people's lips, a lot of people are talking about it and seem to be interested in it
The question on most people's lips was not whether there would be war but when itwould it break out.
if a question or comment is on someone's lips, they want to ask or say it or are in the process of asking or saying it
He stopped in the dressing room beside their bedroom, hung his coat over the cornerchair, his apology already on his lips.