The book is/lies/sits on the table
"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" :
"Name the verbs in the following sentences and the nouns they say something about
The boys climb the tree
The book lies on the table
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.
For your actual question, it's simple: be is different from all other verbs. It just is.
But I think the more interesting issue is that you say that sit and lie are stative verbs. They would normally be classified as activities, not states, going by the standard tests in a semantics class. They are atelic and can be used with the progressive. But really, just put it out of your mind that the verbs have to be "stative" or fall into any particular category and pay attention to what you read in the class notes you've cited. Linguistic analysis always has weird cases.
I think you don't get an habitual reading with the simple present form (and thus no reading at all) because you are choosing an inanimate subject. Sit and lie derive from posture verbs that normally have a human as subject; it's not surprising that some uses require a subject with agency.