I’m looking into making a foundry for melting lead. I have seen many youtube videos about people using plaster of paris and it crumbling after continuous use. I was wondering if someone could give me some insight on what to use as more of a permanent solution. It would have to be something somewhat small and maybe portable, fuel could be propane or charcoal.
Lead melts at a relatively low temperature, one of the lowest of all metals. If I was needing to melt some lead I would start with an old propane cylinder and cut the top off 
very carefully after making certain it was completely empty.
Lead has a pretty low melting point. Have you looked up some electric foundrys for lead? I have some family that melts and casts lead bullets, here is a link to a youtube video showing it: https://www.youtube.com/watch?v=iMZaiIofVYY
I think he just got his at Cabela’s or something, its a small electric smelting pot with a bottom spout pour. http://www.cabelas.com/product/Lee-Precision-Pro-Pot/1317273.uts?productVariantId=3088751&WT.tsrc=PPC&WT.mc_id=GoogleProductAds&WT.z_mc_id1=03367746&rid=20&gclid=CMGSiaKd6tICFY6Fswodl7QPUw&gclsrc=aw.ds
Were you thinking of something larger?
by the way, I think what you are actually making is called a crucible 
I have the lee bottom pour spout, just looking for something bigger for when I get big pieces of scrap.
For processing reclaimed lead I use a large cast iron pot with propane burner under it.