On-demand lay-flat binding options are few. Joel Friedlander posted on 9/11/17 on the subject, talking like it’s no big deal. This is true, but only in traditional publishing, in most cases.

On-demand lay-flat binding options are few

Joel says, “My conclusion, after quite a bit of research, testing, having prototype books created so I could try to destroy them, is this: sewn bindings will give your book a structural and aesthetic integrity unachievable by other means, and it’s surprisingly affordable from the right vendors. And PUR is the undisputed choice for books that need a flexible binding and permanent adhesion, so it pays to check with your print vendor.” But neither of these options are available to authors or designers using or helping on-demand self-publishers.

Much of the “normal stuff” in traditional printing becomes very hard to do for self-publishers

We really do need to be aware that, even though we get excellent publishing access with the new “free” self-publishers, things like foil stamped/embossed covers, 2-color printing, or lay-flat bindings are simply not available.

Lulu offers the most to us

It offers spiral binding in two paper colors and four sizes: white paper—letter, A4, & A5; cream paper—6×9 trade. But it doesn’t offer the better Wire-o option. It sells them on-demand, BUT Amazon will not take them.

Lightning Source has a large variety of sizes & Wire-O

They have many paper choices also. But they require a 25-copy minimum order. So, it won’t work for on-demand orders.

But none of them offer the better choices

I agree with Joel that the best option is probably smythe-sewn [though I must confess I have not seen a machine-sewn copy yet]. However, there are other options nearly as nice. Here we see machinery for LayFlat Photobooks. But we do not see even the traditional publishers going for this option.