In your first sentence:
"Have you laid the books back in the bookshelf?" – Using "laid" here implies placing the books down more deliberately or carefully, often suggesting an orderly action.
"Have you put the books back in the bookshelf?" – "Put" is more general and doesn’t emphasize any specific way of placing the books. It’s often used as a catch-all verb for "placing" or "moving" something.
The difference is subtle, but "laid" can imply a bit more careful placement than "put."
For synonyms of "to lie" in your examples:
"Between the two cities lie eleven hundred miles."
Synonyms: span, stretch, extend
Revised: "Between the two cities stretch eleven hundred miles."
"She didn’t turn to the Woods; she turned to whatever lies across from it."
Synonyms: exists, is located, rests
Revised: "She didn’t turn to the Woods; she turned to whatever is located across from it."
These synonyms emphasize location or distance in a similar way to "lie."