How deep does the soil need to be for a lawn?

Here's my story. I have two-333 sq foot sections of front...land. Last spring I removed two big stumps with a stump grinder, and that basically destroyed my lawn (which wasn't very good to begin with). I spent last summer installing a french drain and sealing around my foundation as best I can. Now I want to rebuild my lawn, but I want to also divert rain fall away form the center of my house because water is still seeping in there.

What I want to do, is dig about 10 inches deep, slope it to one side, layer it with heavy construction plastic, place about an inch of gravel on top, fill it up with the existing clay until there is about 2 level inches left. Then lay sod. Will that work?

Greg

Hi Greg,
don't be surprised if you not many step up with lawn ideas; most permies are getting rid of them as fast as they can!
I know nothing about complex drainage and construction systems, but I'll say it anyway...do you NEED that plastic ? Introducing an impermeable-ish layer sounds like trouble ahead, but like I said, I know nothing! I'm also in New Zealand and everything's backwards here!