You're describing a book's location at the moment of speaking.
a. The book is on the table (right now).
b. The book lies on the table (right now).
c. The book sits on the table (right now).
I think a. works but b. and c. don't. In order for them to work, they need to be in the progressive (is lying/is sitting).
Aren't 'lie' and 'sit' both stative verbs?
If they are, how do you explain that b. and c. don't work, while a. does?
Note
For those who think b. and c. are grammatical, here is "Class Notes Semantics I & II, UT, Austin, Spring 2015-Spring 2018", which says b. doesn't work (p296):
[b.] doesn’t seem to have any coherent interpretation at all, not even as a
statement of where the book normally is or ought to be.
(In the PDF file, you can search "The book lies on the table" and go right to the page.)
If interested, please read the first two paragraphs on page 296.
Another Note
Here is another linguistics book that says b. doesn't work for describing the moment of speaking.
Linguistic Semantics by William Frawley says:
19a. The book is lying on the table.
…
If (19a), for example, is put in the nonprogressive, a habitual (or nontemporary) interpretation results: The book lies on the table.
Best Answer
"The book lies on the table" is perfectly natural to English speakers. As evidence, this Google books search shows that the phrase "The book lies on the table" was a common example English sentence in both grammar textbooks and books teaching foreign languages.
For instance, this very basic grammar textbook that was apparently originally part of the Harvard College Library reads, in exercise 1 of "section 4 The Verb" :
This is clear evidence that at least one native English speaking grammarian whose work was acceptable to a prominent university felt that the phrase "the book lies on the table" was obvious and simple enough to be used as an example sentence for young children.