You might call the following:

Hudson Booksellers - Store
Description: In addition to a broad selection of bestsellers and new releases, Hudson Booksellers is known for its superior selection of hard cover, paperback, trade, and children's books
Location: After Security | Gate/Area: Gate 30
After Security | Gate/Area: Gate 42A
Hours: 4:45AM -12:30AM
Phone: 310-337-6761

I have seen that some book sellers also carry the kindle in MSP. I don't get to LAX very often.