For trees, I think it varies by species. You definitely do not want compost or mulch covering the root flare of any tree.
On TOH, Roger said to put down one or two inches of compost to revitalize grass and rake it in so that the grass blades still rise up a bit above the compost.
To smother grass, cut it as low as you can, put on cardboard or newspaper then the mulch or compost. Trench around the area if you have surrounding grass that you don't want to recolonize your new planting bed. Some kinds of grass are harder to get rid of by smothering than others. The kinds we tend to have here in the NE are easily smothered but other kinds of grass I hear are harder to smother.

When filling in a low spot in a lawn the best way to do that is to cut the sod, roll it back, fill the depression to just above the level you want, and then put the sod back in place.
How much soil you can put down depends. If what you have is heavy, compacted clay and you are putting more of that down a couple of inches is about all you could do, but if your soil is sand and you are putting down more sand you could probably go 4 inches.
How much organic matter is in the soil you have?

The light bulb came on. Why didn't I think of cutting back the sod? It's only a spot about 6x6 feet around.

The trees around this area are a Brandon Cedar and I think the other one is some type of ash tree. They're on the outer edges of this low spot. The cedar has been there probably 25 years, and the ash maybe 35. We planted an Amur Maple last year near the other edge of the dip. The maple is within an area where I built it up about 4 inches and surrounded it with bricks to contain the soil.

We have crappy clay soil with about 4 inches of topsoil. I used all my compost in other areas last year, so there's no organic matter at all, except a spot beyond the low part.

From what the responses are, probably lifting the sod, filling it in, and then slowly adding organic matter to the top would be my best plan of action. Right?

Or....could I kill the grass with cardboard, and do a shallow lasagna bed and plant hostas? As long as it's shallow enough, would the trees adapt? And, if I did this, could I build it up even more as the years go by if I want to?

Where is the love ????

Post a pic ;-)

A picture is worth a thousand words ! !

I wanna see..... Babyyyyyyyyy

It would be nice if I could post pictures. The crappy computer and the older camera I have won't work together.

Besides, the spot I'm talking about is covered in 3 feet of snow right now ! Yikes! Planning ahead.........

Yikes ;-)

If it under 3 feet of snow right now, maybe it filled in on its own... yeah... let's go with that ;-)