You can make your Leanpub book available for people to read online, without having to make a purchase, by going here:
...making sure to replace YOUR_BOOK with your book's unique web address.
On that page, you'll see this section:
Tick "The full book" and click the blue "Update Book" button at the bottom of the page.
Now, if you go to the landing page for your book, you will see that people have a "Free to read online" option to the left of the book cover, under the title and description (see the bottom of the following screenshot):