It is amazing how much soil you can put on top of a lawn and have the grass work it's way up to the top. I had a full septic install, the whole yard was churned, scraped and covered, yet there are original lawn grasses coming through in a certain area.
To level an area I'd just add soil, even up to four to six inches (anything more than that I think would pretty much kill existing grasses). If you don't want to wait for the original lawn grasses to come through then seed those areas. I've done this before with great success. It may look blotchy for awhile, but it evens out pretty quickly. Youre biggest problem with be matching the existing grass. This lawn here was covered with fine fescue because it was mostly shaded, now most is in full sun. I use a seed called Rebel, it's a mix that is supposed to be good in shade or sun, and is somewhat drought tolerant. I will say the lawn is fairly green all summer, even through drought. The Rebel is hardy and grows fast enough that it's taken over most of the lawn, now, from the patches I've done over the years.