Your first picture looks more like a stack of lumber than sheets of veneer. If the veneer has actually warped that much due to sitting outside absorbing moisture, then moisture is what it will take to get them smoothed into the shape you're looking for.
I would suggest making a form to wrap the veneer around, then steam or even soak the wood until it's soft enough to bend without breaking. Wrap the softened wood around the form, then attach the edges and set it aside to dry.
If you're planning on gluing an overlap, you could use a Gorilla™ type glue that will activate with the moisture in the wood and stick, otherwise, you'll probably need to clamp the veneer in place on the form and wait until it's dry to do the actual gluing.
If you're planning on very small
nails brads to hold it together, you might be able to inlay a piece of metal into your form as a nailing backer to bend your brads over as they go through.
Once the veneer has dried, slip it out of the form, et voila! Lamp shade!
To give you something to mount the bulb-base and hanger to, I'd suggest cutting a disk of wood that you would slip in from the bottom end and affix (glue or brads, to match) to the top. To give the bottom some strength and shape holding, you could either use a disk as at the top, or cut a hole in the disk to allow some additional light to come out the bottom.
No matter how you do it, this sounds like a neat project, and I hope you'll come back to update us with your progress & final result.