I work large estate properties in south louisiana.
eventually, you find areas where the clay, sand, and nutrients, or water table just can't sustain normal grass growth. There are just so many factors involved. Ultimately, in problem areas, I take the long term approach...plant test plots with multiple different varieties of grass and see which will grow and endure. In areas, where I need grass to grow quickly in order to fill in exposed soil and prevent erosion, my go to is perennial rye. eventually the zoysia and augustine will overtake it, but it works well to "patch" areas, where we have done dirt work.
another technique is to locate the closest area on the surrounding lawn where the grass is living well and then take a plugs from that and transfer them to the problem areas.. If that doesn't work, then you know pretty much that you are dealing with some kind of nutrient starved soil and it's unlikely anything is going to grow there unless you address that first. I'll give you an example: we have a few places that are near surface springs...always wet just inches below the soil. The bacterial and fungal and mold growth is too toxic for grass growth. For that area, we had to come up with a completely different way to landscape and eventually decided to simple grow bushes and small trees. Some areas we learned could not support growth at all, no matter what we planted and transplanted and we concluded that at some point that area was contaminated or contained naturally occuring heavy metals, toxins, domestic animal runoff, old sewer/septic systems, and even industrial waste. There can also be infestation of nematodes that will destroy new grass growth which can be hard to detect (and yet, pretty easy to control..I use dawn liquid soap!).
You can have the soil chemically diagnosed, yes, but ultimately you are going to have to test what grass and what treatment and what conditions are best to establish new lawn grass. That just takes experimenting. I would go with perennial rye because it is very hardy, grows quickly and is a cheap and will not break the bank if you find even rye isn't going to grow there.