After you find Lemon's diary you notice the pages are blank!
Or at least the pages appear blank... Check out the conspicuously open book for hints. Look at it. Twice.
The open book said that there's a technique of invisible ink by using lemon juice. The text can be read by bringing the paper close to a source of heat.
Warm up the pages in the diary. But not too much! There's a lighter on the kitchen table, btw.
You can't use the lighter on the book, directly. Use the lighter to light something else up. ?
Use the lighter on the incense stick to light it up.
Show the diary to the stick to read it.