I can't work out why Lean Out is necessary in the example given in the rule book. Can troops not look straight down, or is this just a bad example?
The diagram isn't great. It mostly kicks in where there is a parapet that's thick enough to block LoF to the base of the building, or any kind of overhang.
you can also use it to look around corners if buildings are lined up in such a way that you need that little bit of a lean to see around the neighbouring structure.
Basically, the book's diagrams are not to scale for height anywhere. Use them for illustrative purposes only and not for measurements.