I put these together today - I made a very different spout for one - I had seen it on a website so we'll see how it works...
To make a lid throw a 'bowl' with a narrow base and a flanged lip. Measure carefully with the calipers to make sure it will fit in the pot. With the lid still stuck to the bat you can see if they fit together by gently setting the lid into the pot.
When the lid is leather soft a top of pulled clay ribbons.