Aunt Lake is apparently the actual aunt, or perhaps great-aunt, of Eustace Blint, but insists that everyone else call her "Aunt Lake" as well. (Since "Gramps" Gorbuckle is Eustace's great-uncle, this presumably means he and Aunt Lake are related in some way, but if so it's not clear exactly what their relationship is... certainly it's not anything as simple as husband and wife or brother and sister.)
Also unclear is whether "Lake" is actually her name, or a descriptive title. Aunt Lake's body is hollow and apparently much larger on the inside than its outside dimensions would appear to make possible, and she does in fact have inside her a vast quantity of water, inhabited by fish and other aquatic life... in short, a lake. She doesn't seem to object to other residents entering her lake, and it's not uncommon for boating or fishing trips to take place there... what's inside Aunt Lake for all practical purposes seems like a typical lake well suited for recreational use, with the odd distinction of being surrounded by flesh.