Though I can't speak to the "normal" household or that my answer is even among the earliest concordances, I would point out a certain body of literature on mowing and, more broadly, gardening proliferates throughout early modern Britain.

Andrew Marvell, for example, wrote a series of poems on "The Mower" that, though they fill pastoral conventions, draw attention to the 17th century mower and his scythe. However, Marvell was a politician and belonged to a more prestigious class than the individuals you asked for. Another literary tradition of the time were country house poems (Marvell's Upon Appleton; Ben Jonson's To Penshurst). Again, these are landed nobility - but they too suggest emphasis on horticulture before the mechanical lawnmower.

That's not to say mowing was purely "noble" pursuit. Literary scholarship tends to focus more broadly on gardening than mowing, but overlap exists. Rebecca Bushnell has written about the flowering of gardening manuals readily available. Sarah Knight's Reading Green in Early Modern English talks about literal and metaphorical mowing. More casual is this anonymously published 1678 pamphlet about a farmer underpaying a mower.

The short answer is that lawns, just as lawns, are quite a modern thing - basically invented in the US alongside suburbia.

The longer answer has a number of components. First, lawns are somewhat alien to many climates. They're fine in the British Isles, where it rains all the time, and your lawn remains green. In Southern Europe, it can take considerable effort to keep grass green in summer, and in Northern Europe, it vanishes under snow (or just dies off from severe frost) for an appreciable portion of the year. Across much of the US, it costs obscene amounts of money to keep lawns green. The space for a lawn would have been more usefully used in most cultures either as pasture for a goat or cow, as garden space to grow vegetables, or as an orchard, from which hay would have been cut once or twice a year. Or just as yard space. The English cottage garden is the another form of beautifying the space between the house and the road.

Next, there were what you might term accidental lawns in big estates, where grazing animals kept the grass short, and there was that cropped grass just after hay had been cut - this is where the mower than /u/kadune/ refers to comes in. Rather than being an aesthetic practice, it was an agricultural production practice - but the neatness of the post-mowing field is appealing. There were areas of grass kept short near the house on estates, too, but these weren't quite the sea of green that we now think of - instead they were part of an overall garden plan, often with flowerbeds in the middle of them, or even whole shrubberies, in a way you still see in parks in the British Isles. And they were also used for lawn games, picnics, and so on - again, specific uses, rather an overall look.

A book called The Art of Beautifying Suburban Home Grounds, published in 1870, seems to have been one of the main factors in popularising the lawn in America, with the line:

"A smooth, closely shaven surface of grass is by far the most essential element of beauty on the grounds of a suburban house."

Lawns then spread from the US to other parts of the world, and they now look 'prosperous' by association - so that you see them in Southern Europe, in India, in Australia, and in other places where they're really, really not suitable landscaping.

Sources:

Michel Pollan, 'Why Mow? The Case Against Lawns', New York Times Magazine, May 28, 1989.

Vera. K. Ninez, Household Gardens: Theoretical Considerations on an Old Survival Strategy (1984)