I know that the family skillet lids are interchangeable. However, I do not know about the other pieces. Sorry!

 

I think if you use a lid from the same size pan it will work. I just put the Professional 2 qt lid on the Generation II 2 qt pan, and it fit. (I do not have both full sets to try all the pans.) Each set has slightly different sized pans, so those obviously would not fit. They also have some that are the same--the 2 qt and the 10" skillet. I know the 2 qt lid fits both and the family skillet lid fits both, so I assume the 10" skillet fits both. Hope that helps!