I have not worked in Peru in a couple of years, but spent six years working in country - mostly in the bush doing mineral exploration work. I lived in the States and commuted regularly. However, during that time I spent considerable time in Lima transiting to and from other parts of the country.

As others have said, Lima is a vast mixture of areas, some quite safe and very upscale, others you want no part of. Also, as others have said, there is poverty and the there is abject third world poverty of the kind that can be found in Peru including parts of Lima. I must admit, that I avoided the worst parts of Lima as there is really no reason for a gringo to wander around there.

You were given good advice about learning all you can about the poeple who will be leading the trip. You should also inquire as to what parts of Lima they expect to visit and work. When they speak of a "slum" they may be speaking more of the lower income parts of Lima, not the truely dangerous shanty towns that popped up during the height of the Sendero. An American idea of a "slum" and a Lima shanty town are quite different.

If your daughter goes, she will be in for an eye opening experience unlike anything she could gain here in the US. I took my oldest son with me on one of my trips a few years ago just so he could gain an understanding of just what true poverty can look like. He still talks about it today. My advice would be to check things out well, and if you feel relatively comfortable with things to let her go. All in all, Lima is a fairly safe place these days and has improved considerably from the years when I was picked up at the airport by armed security personnel. I would have no qualms about letting someone in my family go on such as trip as long as they were to stay out of the very worst parts of town which I suspect they will - parks, schools and open air markets can (obviously) be found throughout Lima. Maybe you could go with her and gain the experience as well.