What is the ruling on lying to a person afflicted with dementia (Alzheimer's) to avoid harming them, such as saying, "I'm going out and will be back shortly," if one intends to go to the city, or "They are fine," when asked about the deceased, especially if one is unable to use tawriyah (ambiguity/double entendre)?

Lying is fundamentally forbidden, but indirect speech (ma'arid) can be used instead. If harm cannot be avoided except through lying, then there is no sin in it, according to the hadith: "He is not a liar who reconciles between people, saying good things and promoting good." The Prophet (peace be upon him) permitted lying in three situations: war, reconciling between people, and a man speaking to his wife or a woman to her husband. Speech is a means to achieve objectives, so if a praiseworthy objective cannot be achieved except through lying, then it is permissible. If the objective is obligatory, then lying becomes obligatory.