A few of us on our street have "black clay spots" where grass doesn't
grow or grows quite thin.

Someone recomended a lime based product which would cure this.

What is the black "stuff" and anyone ever heard of the lime treatment
being suggested?

These are new construction houses/ new lawns. Would you do the lime
treatment before or after planting grass (too late, grass is already
planted, but feel free to answer), before or after starter fertilzer
and is this going to be a recurring problem?