If the pot is subject to oxidation on the outside and inside when it is empty, then, IMHO, leaving some lead in the pot will protect the base metal of the pot from oxidation, similar to tinning an iron. You always leave the tip of an iron tinned afterwards and tin it before starting a new job.
Interesting thing about the cast iron pots, you can't tin them on a bet. They seem to repel the lead. If lead is left to cool in the pot, when the pot and lead is cool, just turn the pot upside down to empty it. The lead falls out as it does not grab onto the pot at all. If you pour all the lead out of a pot it all goes out, none is left on the surface of the pot. IOW no tinned surface remains.
In the dry climate I reside in my pots never rust just sitting around as long as they are indoors and don't get actual water, as from rain, on them. Let them get wet and see how quickly they rust. I don't know how they would do in areas that have high humidity. In any event, when you melt lead in them, the oxidation comes off and can be skimmed off when you flux. I guess it won't hurt a thing to spray a protective cover of oil on your pot when in storage to keep the rust off. It would just act as flux and burn off when you heat it up again.