Is it feasible to grow edible crops for lawns?
There are lots of things that you can eat that you could grow as a lawn.  That probably are growing in your lawn now.  My yard is about half violets and they are edible.  Purslane is a delicious succulent lawn weed.  Grab some, rinse it off and eat it.  It is crunchy!  I am telling you from experience you can eat a lot of it and you will not get sick.

 
Purslane image from here.
http://www.livescience.com/15322-healthiest-backyard-weeds.html

This backyard weeds link says lambs quarters are edible and I did not know that.  They are also volunteers but I did not know they were good for anything and so I was pulling them up.

We are surrounded by things we could eat and which our ancestors ate all the time but which we do not eat.  If you are in school, Johnathan, and this sort of thing interests you it would be a stellar project.  You have all summer to grow weeds in pots and then at the science fair you could have people taste them.