https://etymology.en-academic.com/27820/plumb

plumb plumb {{11}}plumb (adj.) "perpendicular, vertical," mid-15c., from PLUMB (Cf. plumb) (n.). The notion of "exact measurement" led to extended sense of "completely, downright" (1748), sometimes spelled plump or plunk.

{{12}}plumb (n.) c.1300, "lead hung on a string to show the vertical line," from O.Fr. plombe, plomme "sounding lead," from L.L. plumba, originally plural of L. plumbum "lead," the metal, of unknown origin, related to Gk. molybdos "lead"

Neither have anything to do with pouring molten lead. Only measuring the vertical.

The purpose of finding the vertical is to determine the horizontal in installing sloped pipe.