> "I applied some lime to bring the ph back"

Did a soil test from an accredited facility recommend the lime or were you just trying something/anything?

What was the underlying soil like before the sod was layed? How much organic matter was in that soil? How well did that soil drain? How well did that soil retain moisture? What did that soil smell like? What kind of life was in that soil?
What did a good, reliable soil test tell you about that soil? pH? Nutrient levels?

I put the lime on because the vinegar is acid and the meter suggested that the patches were around 6 and the surrounding areas are 6.5.

Let me be clearer, although I didn't want to lead anyone into an answer. Chemical ferts will cause alot of initial growth. Does organices cause the young seedlings to grow at a slower rate?

Most all grasses grow best with a soil pH between 6.2 and 6.8. If you have your own pH meter how well that will work and whether it will really give a good reading depends on many things, but mostly those are not very reliable.
Organic "fertilizers" can give the same results as the synthetic fertilizers but what you want to do is make the soil into a good and healthy soil that will grow strong and healthy plants without the need for "fertilziers".
Contact your county office of the North Carolina state University USDA Cooperative Extension Service about having a good, reliable soil test done so you know what your soils pH is and what the base nutrient load is and then dig in with these simple soil tests,
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 you 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.
to see what else needs be done with your soil to make it into that good, healthy soil that will grow strong and healthy plants.

Here is a link that might be useful: NCSU CES

I put the lime on because the vinegar is acid and the meter suggested that the patches were around 6 and the surrounding areas are 6.5.

Assuming you only sprayed the foliage, there is no need to counter act the acidity of the vinegar. It should have never touched the soil.

Let me be clearer, although I didn't want to lead anyone into an answer. Chemical ferts will cause alot of initial growth. Does organices cause the young seedlings to grow at a slower rate?

An organic program will control growth. You should not get the type of run-away growth you can see in chemical programs. Sometimes when you are first starting you might see run-away growth as the soil microbes adjust to it, but that soon ends.

What type of grass do you have and where do you live? With NC in your handle I might assume you live in North Carolina but I've been fooled before.