Currently, it's not possible to remove books from you bookshelf. But if there is a book you don't want your other awesome Lix user buddies to see, you can always hide it.
Simply click on the tree-dotted icon (circled in red, below) and a window will pop up with an option to 'hide book'. Voilà , your book will be hidden.
To access those hidden books, turn off the 'Only show hidden books' icon (circled in red below). You will now be able to access your super secret hidden books. This functions works like a toggle—if you switch it on, the hidden books will be visible, and if if you switch it off, they won't. Easy peasy!