Here are some of the ones that I found (note: some of these are meant for children, but I'm not a book snob when it comes to age groups and neither am I a lamp snob. If it's interesting, I'm in).
This group from Etsy intrigue me just because they look like books. Not sure how much light they give out.
Another book-shaped light. This one can be personalized. It comes in different sizes and can be used standing, on its back fanned out, or even opened to a full 360 degrees.
This one looks like a lemon. How fun is that? Available at Amazon, it comes in different colors and also different shapes (a honeybee-type and a sort of rabbit. You'd have to click through to see what I mean by those shapes. A bit of artistic license going on there).
The Krux lamp from IKEA looks like a puppy (I think).
This flower lamp comes in multiple colors (two at the link below, but elsewhere on the website there's also a green one).
There are numerous lamps similar to this dog table lamp (a person running, for example). They're adjustable.
There are a lot of fun robot lamps of various styles on Etsy and Amazon (do a search on each site to see what I mean). Here's one. This might be fun, especially if you're into steampunk.
(This lamp appears to have sold, but if you Google robot lamp, you'll find other versions)
You can also get a personalized folding lamp. (Or you can find plain folding lamps.
If that isn't enough to get you started, try going to either Amazon or Etsy (or just Google) and looking for owl lamps, Harry Potter lamps, folding table lamp, flower lamp, LEGO lamps, or whatever your imagination can come up with. There are tons of ideas out there.
Have fun searching!