They wouldn't have painted over because of the lead paint. They would have painted because they didn't like the color, or because the paint had gotten ratty. Very few people consider lead paint to be an emergency. It's lead, not plutonium.
The issue with lead paint was found because of a socially motivated race to find causes for several groups doing poorly on intelligence testing. Turns out children eat paint chips. Middle-classers live in well-kept, often newer homes which had no peeling paint. But the urban poor live in older, rental (so maintenance is not allowed) slums with peeling paint. Lead poisoning causes brain damage. In a house with well-maintained paint, it's not really much of a problem; however, it's politically unpalatable to say why that's so.
So, make sure the paint is stable and not likely to peel. Then just go ahead and overcoat it.
You can strip it if you want to, but paint old enough to be leaden is also old enough to be alkyd. This can be a little challenging to strip; the overcoated latex will come right off but the underlying alkyd will fight you. Heat can help, but keep it under 1100F. If you sand, wet-sand, and send the wash and solid chips to wherever your town tells you to.