You want a foam that has closed cells (not pressboard or white styrofoam). If you get a foam that will hold water, you will have a mildewed, non-effective mess on your hands unless you have a very casually used, non-refrigerated "cold box" that is usually left open and without anything in it.

The problem occurs when the due point within the insulation system becomes saturated with moisture which is condensing. You can't just depend on a moisture barrier to keep the system dry. Once you have moisture you'll have mildew, the water or moist board will reduce the effectiveness of the insulation system, etc., etc.

As I recall, "Blue Board" was such a material.

P.S. - I've had a Glacier Bay insulation system from over 10 years. They make very effective lid assemblies (or they used too, anyway).