It's the dust that's the worst. Use a chemical stripper rather than sanding. If you must sand, do it wet, and clean clean clean so that you don't bring lead dust into your house, your laundry, or eat it with your sandwich at lunch when handling food with your contaminated fingers... A good hit of lead will mess you up right away. For a body filler made prior to epoxy chemistry, there may well be fiber in it, too. The upside is the latency period for asbestos is up to 40 years, so if you're already in your fifties, you will probably die of natural causes before you die from the exposure.
OSHA has good tech manuals on their site on how to control exposure to both substances. It's worth a look to understand the nature of what you might encounter when working on pre-1980-ish paints and probable asbestos containing materials.