Yes, caring for patients with Alzheimer's is quite challenging.
Regarding "therapeutic lying," it may be helpful to address the question of "who's needs are we trying to meet?" Our need may be for the person to be alert and oriented to person, place and time as much as possible. However, the person may, as you mentioned, need comfort and perceived safety. In that case, offering comfort is the higher priority, as your intention is to meet the person's need.
Regarding "hope:" In hospice, families would often ask the staff, "Is there any hope?" What we offered was that, yes, there is hope. Not hope for a cure, as there may not be a medical cure, but hope that the person will have good days, have loving family present, be pain free and as comfortable as possible. The focus of hope shifts from cure to comfort. Many families found this helpful. Perhaps your Alzheimer's families would, too.
Thank you for your kindness and concern in such a difficult situation. May you receive much merit!