Come to think of it -
Living in suburbia with a lawn is part of what was packaged as the American Dream when the automobile came into existence and gasoline was cheap. One could work in the industrial cities without actually having to live close to it, or in it - instead having a refuge of sorts away from the big, noisy and dirty city - in a suburb - where it was quieter, cleaner, away from large industry but still close enough to benefit from industrialization and large subsidized agricultural farming. A lawn and maybe some trees and shrubbery is the nature that was sold as the refuge from city life. No need for anything like real farming - that's mostly done either by the State and/or large corporations. They create the food, and market the processed stuff out to the masses - most everyone works to buy it, and because of this, they have what basically amounts to a monopoly on which almost everyone is dependent. In this context - a lawn taking up most people's suburban land space suits them just fine. You can't eat it. It doesn't require all that much knowledge to maintain and it keeps people like me buying gasoline for my mower and whipper snipper, and roundup to kill the weeds. More things I have to pay for for the benefit of looking at some green land.
If you look into it - many suburbs have restrictions against growing anything but lawn and a few trees and shrubs - specifically restrictions against growing food - at least anything more than a little garden plot. If it's for aesthetics by some, that's only because of tradition for the last 70 years or so. No one looks at my long grass and complains. Or anyone else's. But some people do complain if people start converting their lawns to growing grains and vegetables. And sometimes the local city puts up a stink and tries to shut people down doing that too. "You may have a lawn - you may not use your land to sustain yourself in any significant way". That would interfere with too many monopolies.
There ya go. That's my long winded answer to your question of when the lawn came into existence as a staple for suburban living.
One might deduce that my yard is full of vegetables. No. I have grown different ones here and there - but anything larger scale I haven't made great efforts to. That is something I do want to change though.