Thanks Steeve. To answer your question there is many ways to clean a litho piece and I do not think there is a really good one, no magical product exist.
What I do first is a very soft cleaning with fresh water and dish-washing detergent product, using a very soft paint brush. After rinse with fresh water and a little heating with an hair dryer to remove humidity. After I pass a light coat of very fine oil to stop the rust and after one or two days is remove all the excess oil with a very soft cloth. I do not use wax or anything more. That's the way I have cleaned that station and the result is not too bad, of course there is still some rust on the roofs but it will not rust anymore.
One very important thing is always to try in a hidden place to see what happens, litho parts are made from ink and so many surprises are possible that you have to be careful. When it is damaged it is too late to make something good.
Very best, Daniel