Personally I don't use any cleaner on the lid. First I remove the Weber emblem. Then I Go over everything that I can reach easy with the lid on the grill with the razor blade and then I take the lid off the grill place it upside down on a soft towel and continue to work on it with the razor blade scraper until I've got everything I can reach with the end caps on. I like to leave the end caps on as long as possible because it keeps the lid more rigid and sturdy. Then I take the end caps off to get everything I can with the razor scraper. Next step I use 0000 steel wool to get any tiny spots missed or in the nooks and crannies at the edges inside the lid. Then I take my rubbing compound and go over both sides of the lid really well to get anything I may have missed with the steel wool. Then I go over both sides with a good coat of wax.
This is not necessarily the right way to do it it's just one of many ways it can be done. It works well for me and maybe just some ideas for you as a starting point.