Paints made and sold NOW are all lead-free unless they are for specific uses. If they have any lead in them, it should say so on the tin. Old paints often contained lead, so if you are sanding old paintwork, be aware and don't breathe in the dust. Wear a mask.
Children's cots, furniture and toys, in particular, should have all paint removed, down to bare wood, before they are undercoated and repainted with child-safe paints - small children chew and suck on things. Lead poisoning can affect children's brains and development.
In the past, women's cosmetics and theatrical make-up used to contain lead, as they made the skin look paler. That led to lead poisoning, too.