Is it illegal to lock my wife in our house?

Of course you can lock the doors to your own home. If not to keep your wife from wondering, but to keep you and your property safe. I agree with JesseBelle - contact her doctor and hopefully he or she can prescribe meds to calm her and /or help her sleep. She may now need to go into Memory Care at a NH where there is 24 hour care.

Yes, you can lock the doors to the house as long as you are home in the event of an emergency. When someone has advanced dementia, it isn't really freedom that makes them roam. It is disorientation and the loss of things that are familiar. They can't recognize clues that help them find their way home. It is not cruel to lock the doors. You are also saving the neighbors and police some worry. Neighbors would be uneasy if they see your wife wandering in the middle of the night. If the police are summoned frequently, they may insist that you find some way to keep your wife inside so she will be safe.

Perhaps the doctors can find something that can help her sleep through the night. That would be the ideal solution. I don't think wandering around the house or the neighborhood is particularly pleasant for someone with Alzheimer's. I could be wrong, but it seems that way to me.

I assume you mean your wife has Alzheimer's (ALZ), not Amyotrophic Lateral Sclerosis (ALS)? Here are a couple of other threads about the subject:

www.agingcare.com/questions/lock-wondering-dementia-dad-room-at-night-158142.htm

www.agingcare.com/questions/is-it-illegal-to-lock-a-person-in-a-house-when-they-might-wander-171797.htm

PS: My wife has a MedicAlert bracelet so the police knows who to call when they find her.