How many lumens needed to light up a lawn using floodlights?
I'm not sure whether we can find any charts for this, since it's very much a subjective thing. I can tell you about my experience... 

My back yard is similar, but maybe a bit larger. It's probably 100' by 75'. On the rear gable of my house is a dual-bulb flood, which I've recently furnished with these 90 watt equivalent LED bulbs. They're as bright as the original bulbs and at only 15w. They light up about 1/3 of the yard to the level you describe. 

Based on that, I strongly suggest a fixture that provides four sockets, each containing bulbs like mine. I think you'll be happy. Obviously, with a single point of origin, you'll have hard shadows behind yourself and any objects in the yard. That would take a different solution, though.