Yes, she can run away from it, and if she goes to a different floor/another dungeon, it won't chase after her in there and will leave her alone the rest of the night.
It will... do its best swimming in the lake, but it'll be a lot slower then. If 45 teases the Reaper by having it swim after her for more than two minutes, it's going to cast Hamaon on her to kick her out. I can't believe 45 would bully the Reaper.