My no-dig area of the garden was set up over some of the lawn area, back about 4 years ago and I have never regretted cutting down the size of the lawn. I'd rather harvest food than have a big lawn area.
This year I am going to have a crop of corn and tomatoes in some of the areas. This will be my first time growing corn in the no-dig garden as I needed to build up the area with soil, so it can support the tall corn stalks.
With all the chicken & rabbit litter, I am never short of compost or spoilt straw for topping up the area when needed.