Dishwasher safe lids for copper cookware

Modern stainless steel pans with clad bottoms can be as good as copper pans.  McGee developed a simple technique to test the heat distribution where he fits a piece of paper to the bottom of the pan, placing the pan over a burner and carefully watching how the paper browns.  Thick aluminum, clad bottom stainless, and copper all worked equally well. 

There are differences that relate to the techniques used in cooking.  A thin copper pan is great for melting butter or chocolate straight on the burner.  Modern air-gap wall stainless steel pans hold the heat better and work better for simmering or boiling.  Copper is harder to upkeep.

Pans will develop hot spots, even copper which is the better conductor. Until we get graphite added to the cladding  or some other exotic material to distribute the heat, thickness will matter the most for even heat distribution.

I have read several consumer tests and reviews of pans and they fail to note that thermal conductivity and thickness can both be used in practice to balance the temperature distribution and heat flux in a pan.

If a magnet sticks to it, it's ferrous.

I'd like to give a more elaborate answer, but there isn't anything more to it.