My mom is in memory care lock down community.

It sounds like she gets to go out with the dog, but then doesn't want to return to where she is supposed to be. Is that why she is discouraged from leaving with the dog?

If your mom is having trouble with these outings, I might consider if she is able to handle it. If they are causing her distress, I might consider if it's worth it.

Sometimes the dog
Walker will take her with her for the walk but then my mom wants to stay outside or
Downstairs and not go back to her floor.

Are you saying that the dog is in the facility with her?

Is it impossible for your mother to accompany the dog walker? Is she physically able to do that? Memory care isn't prison. Discuss possible solutions with her care team.