Thank you Speedball for such a speedy response - but I'm still having problems!
I took out the pieces. I adjusted it as far up as it the threaded post would go. I found that although the lever now caught, I didn't notice a huge difference in the drainage. So I tried to adjust it longer, but it didn't help either. I took it completely out and ran water and it still drained too slow. So I'm thinking maybe a hairball is in there - in combination with the trip adjustment. I'm going to the store and find some drain cleaner to see if that with the adjustment will work. The faceplate is pretty corroded, so perhaps I can replace this also.
I appreicate your advice - it gave me the confidence to try to repair it. Any thoughts on a drain cleaner?