Lauren's notebook, which is located at the far left of the menu bar, isn't just a passive receptor of ideas. It's also a place where you can go to stimulate Lauren's thinking and draw conclusions about the things she sees. To do this, open the notebook (outside of a conversation), then click on the two ideas you want to associate. If Lauren finds any brilliant connections between the two items, she'll say so, and you'll have a new topic in the notebook.
There are a couple of places in the game where you can't progress until you help Lauren draw conclusions with the notebook. I'll tell you what to do in those spots.
Unlike normal walkthroughs, in Nice Game Hints you can select just the puzzle you want hints for. Here are listed the puzzles for "How does the notebook work?" in Blackwell Unbound. The guide you choose only contains information about that puzzle, reducing possible spoilers for other puzzles.