Epublib is licensed under the GNU Lesser General Public License.

This means that you can use epublib with both open-source and proprietary software.
The only requirement is that when you distribute your program you have to make the source of epublib available (putting a link in your documentation is fine) and if you modify epublib (bug-fixes, new features, etc) you must also make these available.
You do not have to make the source code of your application available.

For the full text of the license see here:

For why the LGPL works fine for java libraries see here: