Hi Jane,
One of my first recommendations is Grandma's Secret Spot Remover. I have seen it at Hancock Fabrics and JoAnn Fabrics.
Rust is just one item on the list of stains it says it can remove.
Their website is: www.grandmassoap.com
You might try making a paste of Oxyclean type product and working the stain with a washcloth. Another product to try would be Dawn dish soap again working with a washcloth.
I would test any thing that you try by using it first in a very small area. You might have some results with the lemon juice but I would avoid sunlight.
Good luck with task of getting the stains removed. Please keep us updated as you progress through this challenge.
Pam M