Was the recommended amount of lime the result of a good reliable soil test? I seldom see a recommendation for applying lime twice a year except from a salesperson. The best time to apply lime is fall.
While it may be difficult what your soil needs is organic matter and in your area and that you seldom see temperatures low enough to slow the Soil Food Web so any organic matter in the soil is going to be worked on year around.
A good reliable soil test that gives you soil pH as well as major nutrients (P, K, Ca, Mg) and can show the balance between them is one tool that can help. These simple soil tests can also be a tool that could help.
1) Soil test for organic matter. 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. For example, 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 drainsâ 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.

I already had the soil test.

It was recommended that applying 100 pds of lime all at once was too much and I shoud apply in 2 separate intervals.

My main question is really how do you get organic matter into the ground on an existing soil? I am afraid that there is so little actual grass left in this area that I might just 'start over'.

I notice Home Depot near my house just got a big shipment of fresh St. Aug sod. I think I am just going to go ahead and break up my existing soil and add soil conditioner, sharp sand, composted manure and then sod over the top. Now that I have hopefully corrected the drainage problem I wont get the anaerobic problems which basically kllled the lawn before. Add to that actually improving the subsoil before laying the sod this time should help.

I know many are proponents of no till and I agree with that to a certain extent, but how do you successfully do that with a lawn situation. It's not like a perennial bed where you can layer mulch on top of the soil surface. It this was an out of the way spot I might consider layering a heavy orgainc mulch on top of the soil for a year to let the soil improve before re-sodding, but this area I am dealing with is right outside my back door off the patio. Tired of the dog tracking dirt into the house from the mostly bare ground outside!

Short of tilling there is no easy way to get adequate amounts of organic matter into soil. Although the norm is to till and wait a week or two and till again then more waiting before laying sod I have seen it done, laying of sod, right after the first and only till. Results usually are not all that good but it does solve an immediate problem such as yours. Settling, "weeds", unevenness of the lawn are things that can happen.