Learn Portuguese (Portugal): Cada leitor leva um livro para lá.

The verb levar means to transport something away from the speaker's current location. Because the readers are taking the books to a different location, indicated by para lá (there), you must use leva. If they were bringing the books to where the speaker is, you would use traz (from trazer).

What is the difference between using leva and vai in this context?

While both imply moving away from the speaker, vai (from ir) is just about the person going somewhere. leva (from levar) means the person is carrying or transporting an object with them. Since the reader is transporting um livro, we need the transport verb levar.

Why does the sentence use lá instead of ali?

Both words mean 'there' and pair well with the away-motion of levar. However, lá implies a location that is further away from both the speaker and the listener, or a place out of sight. ali is typically used for a place that is relatively close and visible.

Could we just say lá instead of para lá?