An LPA cannot be made unless the donor has capacity.   If there is no LPA in place at the time that capacity is lost, the only way that someone can be appointed to act on their behalf either for financial decisions or health and care decisions if via an application to the court of protection to appoint a deputy (a deputy is like an attorney but appointed by the court of protection with powers specifically granted by the court).
For more information about applying to appoint a deputy click here