I hand-set a lot of lead type in a previous life, and I'm just fine now. As long as it's not aerosolized and you avoid eating or breathing it, lead is a non-problem. Just wash your hands. Of course, much lead was aerosolized during the era of leaded gas and kids ate leaded paint chips and those are huge problems.
Molten lead in a linotype machine might be an issue iff it creates lead vapor, but I'm not familiar with the literature on that subject.
The problem with leaded solders is from the corrosion that builds up on the outside surface of the solder wire. The pure lead is not that bad. Since the lead was recently melted in the Linotype case there might not be much of a health issue there.
Generally, lead poisoning is less of an issue for adults. They can slowly work it out of their system (or at least to a place it is not as harmful). The huge problem is with children. Lead poisoning interferes with brain development.
Anyway, wash your hands after touching lead before eating or smoking. They probably didn't know that they had to do that back in the days when Linotype machines were popular...
Molten lead in a linotype machine might be an issue iff it creates lead vapor, but I'm not familiar with the literature on that subject.