Why would soil always be moist due to the grade? The water has to be coming from somewhere. Is that area a bowl that collects water and does not drain? Lime may or may not be important. You cannot know which kind of lime or how much without a soil test. By using the wrong kind of lime and guessing at the amount, you could set yourself up for a much worse situation. Tilling will set up a problem 3 years in the future. Tilling is popularly used for garden beds. When used on a lawn it creates a bumpy surface after the soil settles. The cheapest soil in the world is sand. I love sand as a base for a lawn. So does every golf course in the country. Your soil can be repaired much more easily than you are thinking. How are you watering? How long and how often? When were the last two times you fertilized?

A more shallow watering, particularly during summer, over tree roots isn't necessarily the worst idea. Those tree roots suck up water like nobody's business, so more frequent watering will be required in this case. We're talking twice a week, maybe three times if the weather is blisteringly hot. It's very hard to keep grass in a shady area! If you use synthetic fertilizer, feed normally--it boosts the grass too much and it's easy to put down excessive nitrogen on lawn that doesn't see enough sun to photosynthesize. Most of the benefit from fertilization goes to the trees, which isn't a mistake. Organically, pour it on. This is less to feed the grass than it is to transform the soil to hold more water. And by all means, use the shampoo. Worst case, it can't hurt. Best case, it'll lighten and loosen the soils and hold more water! Reseeding every fall is probably in your future, grasses really don't like heavy shade. Avoid bluegrass as it loathes even light shade, and favor the fescues as they do better and have deeper roots. It's worth looking into grass varieties that tolerate a little more shade (no grass species tolerates full shade). You'll still need to reseed--just less often! Red creeping fescue might be a good choice for you (it's green, not red!) It's pretty shade tolerant, but...well, you'll need to reseed. Perennial ryegrass is a fast sprouter that'll look good for about a year, but will still need reseeding in fall. Fortunately, reseeding is not difficult and the grass develops so quickly that this might be the simplest answer for you. Plus rye is a nice grass, tolerant of drier conditions, and feels nice underfoot. White Dutch clover is shade tolerant and adding some to your mix will give you a greenery cover at grass height that looks good even when the grass doesn't. You may not want clover, however--I sure understand that!

Large rocks probably should be removed, stones, pebbles most likely do not need to be. The soil particles you have came from those stones and pebbles. In addition to manure and the worm castings your soil will need vegetative waste, somewhere around 6 to 8 percent. With no indication about where in the world you are it is difficult to suggest sources other then there may be deciduous trees with leaves that will become available fairly soon. If you are in the USA your states Agricultural schools Cooperative Extension Service should be able to help with a good, reliable soil test for soil pH, P, K, Ca, Mg levels and these simple soil tests might also be of some help. 1) Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top. 2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains� too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up. 3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart. 4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell. 5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

Put down a weed suppressing membrane first,this will keep the grass and other weeds from growing but will allow water to drain through and away. Then I would suggest 10mm pea shingle. These come in about 25kilo bags and two bags should cover an area of about three foot square at around one to two inches in depth. The bags range from about one pound fifty (pea shingle brown and fawn colour) to ten pound a bag (ALOT smaller bag) of various colours. Blue,green etc. If the area has large bumps and dips it would be good to level it first,if their minor then don't bother unless you want perfection. Best of luck.