lies about reading

They mean slightly different things, but they are both correct when used in the proper context.

No. 1 suggests that the reading activity is current and ongoing. For instance, a columnist in a weekly newspaper or an especially prolific author who churns out lots of books – people might wish to appear up-to-date by claiming to read material which is popular and widely discussed.

No. 2 describes reading activity over time, people's reading history. People who wish to pass themselves off as well-read might say that they've read all the works of Shakespeare, that they loved War and Peace, or that they've read the bible from cover to cover.