You can leave a piece of cast iron in the lye bath for a long period of time because the high pH passivates ferrous metals. It doesn't have to be sodium hydroxide, either. Any alkaline material will do it as long as the pH is high enough. If iron is passivated, that means that it cannot participate in an oxidation reaction, even if oxygen is dissolved into the lye solution. So, if your lye bath pH is high enough (and with sodium hydroxide, it should be) your iron will not rust and the source of the "rusty grease sludge film" isn't your pan unless there is a major contaminant in the lye you are using or you lye bath is shot. If you use a lye bath, you need to keep in mind that the sodium hydroxide reacts with the grease to form soap. If you clean enough pans, all of the lye will be consumed by this reaction.
If you are having problems with lye, you need to contact your supplier and get the spec sheet on what you are buying. Unless you know what is in Rooto, Roebic, and AAA's "food grade" lye, you can run a lot of trials, but what are you going to learn? If you are going to take the time to run trials, consider this scenario. Suppose Skillet A is cleaned in Lye Bath No. 1 and Skillet B is cleaned in Lye Bath No. 2. If Skillet A shows the rusty grease sludge film and Skillet B does not, the experiment did not prove that Lye Bath No. 1 has any more to do with the film that Skillet A does.
