these look like old asbestos brake linings. Not touching them with a 10 foot pole, much less a lathe.....
way back at the dawn of time when dinosaurs still roamed the earth, before law school, I worked as a heavy duty mechanic and welder, usually no gloves, working bare handed, used to blow out the brake hubs on tractor trailers with compressed air, big clouds of brake dust swirling in the air. Welding inside large container vessels, no air supply, no filter masks, maybe a big fan blowing to swirl the heavy metal laden smoke around, bloody hell. At the end of the work day we would stick our bare hands into a big open barrel of Toluene (methylbenzene) and give ourselves a good wash to get all the grime off. No masks, no safety equipment, no idea how toxic Toluene is and how quickly it is absorbed through the skin. The toluene would give you a buzz to send you on your way to the bar.......
couldn't find anyone in Calgary to reline the brake shoes, closest I found to possibly reline them is about a 3 hour drive away, in Edmonton.
https://edbrakeclutch.ca/service/reline/ I talked to them by phone to day, sent them photos and measurements tonight, they will let me know in the next day or two if they can do the reline, they said they needed to check if the tiny little shoes would fit on their equipment. $32 per shoe quoted, plus shipping both ways, so $150 - $200 ish + depending on choice of shipping speed. I can live with that to get a modern non hazardous brake lining material with hopefully better braking performance, if they can do the job.