A picture would be helpful.
Do you make
compost?
Do you have woody material that you want to get rid of?
Not only is that spot all lumpy, but now that soil is seriously compacted. So we need to fix the surface and the stuff under the surface. But, you know, embracing the cheap and lazy path.
My thinking is to dig that area up a bit and then lay in some woody stuff (sticks) and then cover it up with what you dug out. The result should be a little mound. In time, that mound will sorta sink back to flat-ish. If you are following the lawn care article, then by the time it starts to deflate, it should end up a bit level-ish by your other organic matter in the area.
The woody stuff underneath will help with uncompacting the soil in time. If you get it a good two feet deep, that would be good.