According to the linked article, "An average size domestic water tank stands about ten or 12 feet high, and is as many feet in diameter. The water used for drinking and bathing does not come from the bottom of the tank; rather, it is siphoned off the top. The water in the bottom half of the tank is reserved for fire-fighting purposes and is tapped by turning on the fire hoses found in the stairwells of buildings. The necessity for cleaning the tank stems from the fact that water entering the tank from the City's water source contains some foreign matter, which, over time, settles to the bottom of the tank."
http://cooperator.com/articles/202/1/Rooftop-Water-Tanks/Page1.html
I also read that the tanks might fill during periods of low use, like during the early morning hours. Water was constantly cycling through the tanks, her body was not sitting in still water.
As far as the lid, it seems the only person who knows for sure if it was on or off is the maintenance man who discovered her body.