A really good seasoning is the best thing to prevent rust. When I got my first CI Skillet lid, I cleaned it completely, and then I seasoned it just like I season a skillet. Got the lid jet black.
I don't do anything to it other than wash it with warm water and a brush and then dry it with a towel. Anything that gets on it comes right off.
I have only done one "refresh" seasoning on it after about 6 months of use. Wasn't really necessary, but not a lot of extra work as I was already seasoning other skillets that I picked up.
As far a seasoning the lid, you just need to heat it up to about 350, and then apply a very light coat of fat to it. Then wipe off any excess and put it back in the oven for about an hour. After an hour, wipe it off again, and put it back in at 400 for another hour. Then turn off the oven and let it cool inside until it reaches room temp.
The cooling process is just as critical as the heating because molecular changes in the fat are happening that make the chemical bonds strong and make for a good seasoning.
Repeat as necessary until it is seasoned to your liking.
On my Griswolds, there was a tiny bit of fat buildup on the edges of the drip rings, but it only gives it a little bit of a tapered effect.