Yes, Lix works offline. What may vary, is whether your specific books are available offline. It all depends on the different book formats, as some formats are not yet supported offline.
To read a book offline, you need to quickly activate it for offline use. In your book overview, click the blue circle in the top-right corner of the book. Once you click, the red dot on the circle becomes green. This means that your book is now available offline. You can activate up to three books for offline use at a time. You can also view your notes and highlights offline, but they will only be updated once you're back online.