The 30-year-old "Smile" hitmaker has rarely made any public appearance with her husband since June, reported Mirror.
"I will never be beautiful enough to make us beautiful together," the picture posted by her read.
"Hashtagsadface," she captioned the picture.
However, in a statement her rep said, "Lily and Sam are very much together."
The couple have two daughters, Ethel Mary and Marnie Rose, together.