Yes, many Leanpub authors do this. Here's how it works:
For every Leanpub book, you set a Minimum price and a Suggested Price. You can change these prices at any time. The lowest Minimum price is free, and the next lowest Minimum price is $4.99.
Authors who raise the price over time will typically raise the price with each new chapter release. So, when you first publish your book, you could set a Minimum price of free and a Suggested price of (for example) $9.99, and then as you publish new content, you could raise the Minimum price from free to $4.99, then $5.99, etc.
Please note you can set both the Minimum price and the Suggested price to be free at the same time. However, even in that case, readers can still choose to pay for the book if they want to, using our pricing sliders. You may find more readers than you expect will choose to pay you, even if they can choose to get your book for free.