As well as any other tool in the wood shop, a lathe leads you to many new tools. This is great until you have more than about three and need a place to set them so you can pick the right tool, that you need, every time. This is my original design based on inspiration from @torbjornahman and @BlackLabelwoodworks Thank you both for the good ideas.
To cover up the plywood, I used an oak veneer. I wish I would have cut and glued the veneer to the plywood I used first and then glued and screwed all the pieces on top. That would have been much easier.