If testing the soil and aerating it has not helped, you can consider prepping it with compost, DIY or store-bought. It's not too hard to grow a grassy lawn yourself and you can pick the right kind of grasses for where you live. It may be too cold for the grasses you have right now.
There are some other reasons your lawn may be dying. In some cases, white and brown patches may also be caused by a fungus. Fungal spores are naturally present in lawns and if the surroundings are favorable to their growth. Fungal diseases can stick around the soil and the sooner you work on identifying it, the better. If nothing suggested here works, it's worth checking out.
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