Soil tests normally can't tell you much. I've put in thousands of lawns, and I've never done one. Here's the kind of work we do
and a few others
work Photo Gallery by Dan at pbase.com
almost entirely with Christian homeschooled young men.
As has been said, there are so many variables it's hard to know where to begin, as Richard said. Jen is right to ask the kind of soil, though, and you answered with fill dirt.
So, if the irrigation system is right, we need to know what type of grass it is. Fertilizer should be a good lawn fertilizer once per month during the growing season. And since it's fill dirt, use the expensive kind with iron. Proper mowing its the best way to keep down weeds, but we need to know what type of grass you have to advice on how high and how often to mow.