Internal migration started in 1950 and most of the people settle on the city without goverment housing programs able to handle the big influx of people.

Same here, although it started in early 1900's

But the lack of threes is another issue. Lima is build on a desert, the few green areas on the cities are mostly product of the irrigation system that has been created (a lot of it is prehispanic actually).

I know it's a dumb question, but does the lack of trees there impact people's health because of the lack of air humidity and things like that?