Starting with Firefox 57, which will be released in November 2017, only extensions built with the WebExtensions framework will be work in Firefox (see here for details). After investigating what it would take to modify the existing LeechBlock extension to use only WebExtensions, I concluded it would be easier and better to rewrite the extension from the bottom up, reusing existing code wherever possible.
The new extension is called LeechBlock NG (Next Generation). Go here to install the latest version.
Note that this software is under development. It may contain some bugs and it does not (yet) include all the features of the legacy extension. You should disable or remove the legacy extension before installing the new one.
If you want to transfer your settings to the new version, export them to a text file before you uninstall the legacy version (Options > General > Export Options). You can then import them into the new version once you’ve installed it.
The source code for LeechBlock NG is available on GitHub. Please post bug reports there!