I have a 5x12" sheet of Cherry Wood, 1/8" thick, that is not quite flat.
How can I straighten it, and keep it straight?

You could rim it with a really sturdy frame, if not slots in a box then a
thick metal frame. (Sorry, I don't know what a lens board is so I can't
tell if that makes sense in your application.)

Do I need to find a straight piece to start with?

That's your best bet. It's a small enough board.

- Owen -