Does a person sin if he lies to his brother to wake him for prayer after numerous attempts and despair of him waking up, with the prayer time nearing its end, even if the brother does not believe him?

If the lying is for the sake of helping one's brother to perform the prayer, and there is no alternative, then there is no sin in it, Allah willing. However, it is better to use allusions (ma'areedh) to avoid lying.