Gardeners sometimes apply a shallow top-dressing of organic matter or fertile topsoil over an existing lawn. The applied layer is ideally 1/2 inch deep and is raked into the lawn and somewhat incorporated into the thatch and topsoil. A soil layer thicker than 1 inch atop the lawn leads to plant decline or death.
Smothering grass with a thick soil covering can kill the grass completely, but it is a slow process, especially if the grass is perennial and grows by aggressive stolon stems or fleshy roots. Thick soil covering blocks sunlight and weakens the plant, but the roots or stems may continue to grow through the layer to the surface to again sprout leaves.
If you wish to add topsoil to a lawn to improve the lawn, scatter the soil evenly and at 1/2 inch thick. If you wish to choke out and kill the grass, first apply an herbicide to the grass to effectively weaken it and then apply a thick soil layer. This tandem approach increases chances that the grass cannot rebound.