I go to Lima very frequently, and I'm aware of the safety situation. As noted by other posters, some areas in Lima are as safe as any safe neighborhood in the US. But some areas (which, BTW are not too far off) may be extremely dangerous.

That said, the El Pueblo resort is a really nice, upscale place. But you mentioned that her religious group plans to visit slums. Slums in developing countries, and Peru is no exception, can be tremendously depressing. Some slums may be relatively safe, but do you really want your daughter to be exposed to the sights of abject squalor? This can be very, very shocking to her, and I can't emphasize this point enough. I'm an adult guy with life experience, and I think I would be shocked and depressed if I had to see extreme poverty in person.

One smart post above asks how comfortable you feel about the group itself. This is very important. Remember the girl who disappeared in Aruba a few years back? It turned out that the group "chaperones" had a very relaxed and hands-off approach to chaperoning. You don't want that.

I may be terribly wrong, but sometimes I feel that religious missionaries believe that they are somehow protected from crime by divine powers. I don't think so.

Finally, do you think it's OK to go to a Catholic country to try to convince people to switch to your religion? If your targets are poor, and you bring valuable gifts (valuable to them), aren't you abusing your position? Perhaps if the slum dwellers were not so poor, they'd tell you to beat it and respect their religion.

If you want to talk some more, please feel free to send me a PM. But in short, I recommend against this trip.