A lawn is very different to a grazed field.
Here in the UK, in an average garden, you'll have no issues you want to keep a lawn - simply mow once a month at most, and maybe water in the middle of summer. Really isn't hard to look after here - my parents even leave the cuttings where they fall as the worms will pull them into the soil pretty fast if you let them.
Not really true. Depending on rabbit population, or if you have a goat, you can fairly straightforwardly maintain a lawn without mowing. You have to be happy with random rabbit carcasses / holes though. It does take some care (in regards to what you do with fertilizer) if you don't want weeds, but if you keep the land very barren, the only 'weeds' you'll get are wild flowers.
Obviously this all depends on drainage/soil type.
Lawns are historically grazed fields. That's organically maintained I guess, but no one has a lawn like that today, not even in England.