Is it permissible to lie by saying, "This is my sister and not my wife," when someone unexpectedly enters during a video call with one's wife, in order to avoid embarrassment, knowing that the lie carries no ill intention?

A man informing [others] about his wife that she is his sister, without the intention of her being his sister in Islam or anything of that sort, is conveying something contrary to reality and is considered a lie. A Muslim can avoid lying by using tawriya (allusory speech) or ma'arid (ambiguous statements), which means saying words that have an apparent meaning and a hidden meaning, intending the hidden meaning. For example, he could mean "my sister in Islam." It has been reported from the Salaf that in ma'arid there is room to avoid lying.