I spent a couple of decades as a landscape contractor. During that time I've seen more bad lawn installation jobs, than good ones. Most of the failures were due to skipped steps in soil preparation. You will never have a good stand of grass without a deep root system.
The problem with top soil: If you simply pile it on top of your existing soil, without rototilling the two together - you've skipped a very critical step. This part of the process is called making the transition layer.
Without a transition layer, water will be sandwiched between the top soil, and native soil. The water will displace the oxygen the grass roots need, eventually suffocating, and killing your lawn.
Further, topsoil usually has very little organic material in it. Without humus of some kind, there is not a supply of organic matter for roots to reach for, and grow deeply in. The humus also aids in areation of the soil, causing the desired percolation of the water.
I would never install a lawn in topsoil layered on native soil - unless the topsoil was at least 8'' deep. And, in many situations, there is absolutely no need for topsoil. Often it is a bad idea, and an expensive one too. Importing foreign soil to your property will most assuredly bring in a crop of weed seeds you may not already have. Not good.
Our method is to incorporate large quantities of organic matter. If the ground consists of heavy, compacted dirt, we add decomposed granite. Granite contains beneficial rock phosphates, blends well with other materials, and has none of the drawbacks of topsoil.
The boxblade is not a necessary tool for lawn installation, but a good rototiller is. After blending the native soil with the top soil, compost, and fertilizer; a landscape rake with guage wheels will give a very nice finish, knocking down high spots and filling in the low ones. I acutally sow my seed before using the landscape rake in the grading process. After grading, I sow more seed, and lightly rake it into the top 1/8" - 1/4" of soil. Finally, go over the seed bed with a light roller.