Has anyone ever heard of lead used as a sheath on electric cable (romex)?

It was used for extra protection against damage by rodents and physical damage. More expensive than knob and tube but easier to install 2 conductors  in one run.  Most likely  pre WW2 but late 30's for a time period.

Of course. All old cables were wrapped in lead. You know plastic is a recent invention?

Yeah, hell yes. The telephone cables for entire communities were lead sheathed and the individual copper conductors were paper or wood pulp wrapped. These are still functioning direct current cables in use for telecommunications. Prior to what you have, the wires were similarly insulated, but always separated with porcelain knobs and porcelain tubes (where they passed through studs.) You have a rare experiment in home wiring at much higher ac voltage than telephony still uses, get rid of it.

that " cloth " material is woven ASBESTOS .

UK answer. Lead sheathed cable as you have described was commonly used in domestic installations from the 1900s upto the 1940s and the lead sheath was often used for earthing / grounding. During  my working life I have worked in / rewired many properties that were wired in this this type of cable before all rubber sheathed , TRS / Romex type cable, became more popular upto the 1960s, probably due to cost considerations..As you have said the rubber insulation perished and became brittle with with age and this was often the reason for replacing both types with PVC insulated cable.

It used to be standard a long time ago before pvc was developed.

Lead was indeed used a long time ago because it is relatively flexible. That was before we realised how dangerous lead can be. It was also used in domestic water pipes. You may still come across is in very old systems.

Did it look spiral-wrapped? I'd call that "BX" cable. It wasn't all that rare, in houses built though the 1960s, at least.

Not that I ever tested it, but I thought that the outer armor was mild steel, not lead.