I can't help experimenting! So, I did it. I double-dug beds, single dug beds, I lasagna-ed, I interseeded, piled up, strawbaled, and I'm sure a few other things I can't even remember.
The laziest of them all is the over seeding of grain on lawn, which I outline for you here. It is equipment and tillage free, but affective. There's so many ways to attack lawn, but this was my most devious. It's based on knowing how lawn grass grows and out-competing it. There's two ways to do this: One is by winter and other is by spring.
Most lawn grass here stops growing in the cool season. It's more warm season. Most lawn grass is shallow rooted and over-worked (unless it's a permie lawn, which this technique will probably not work). This means it's easy to out-compete by just slightly stacking the odds more against it.
First: Timing. You want to do this when the grass growth is turned off. So, early spring or late fall.
Second: sprinkle with refined compost, soil bed mix, or dirt (this is so less of the grass receives photosynthesis).
Third: take soaked barely or wheat seed and sprinkle them heavily over the ground. Do not mix seed or your harvest will be difficult.
Fourth: Sprinkle again with dirt, so the seeds are covered.
Fifth: cover with straw to shade, but not squash.
Six: Make sure you top-fertilize the grain crop, since the annual roots are shallower and will grab much of it before the perennial grass roots have a chance.
The photo (attached) was done with barely. I harvested about 50% that day (in front of the patch). Total, I got about 4 small loaves of bread from this patch.
I have a row on the side of my house growing now with wheat. If you are doing this within city limits, you may need to put up a temporary fence, so your neighbors know you are not neglecting your lawn.
When the grain grows up, it will naturally die off, leaving not much in the way of grass left, which can then be mowed low and over-seeded with something else.