How to clean and maintain cast iron lids
We use kosher salt to clean (still-warm) cast-iron by pouring in a handful then rubbing around with a (usually paper) towel. The kosher salt grain size is just right to be an abrasive for removing excess grease and other food particles, and you don't have to worry about it melting. Then a wash with hot water and a little soap to complete the washing, followed by a rinse. To avoid rust, we dry the pan by putting it on the stove, high flame, until the water has evaporated.
We have to re-season the pan every once in a while (once or twice a year), but this method has worked well for us.