Yes, you can choose from a limited number of fonts, and you can set different fonts for chapter headings, body text, and code blocks if you are using them. When you are in your Leanpub book tools, select "Writing" on the left, and then choose "Book Theme". If you choose a custom theme, scroll down to adjust the font settings. The next time you preview or publish your book, you will see the new font you've selected in your book.
Want to see what the fonts look like? Then check out the Font Samples section from the manual.