Since it is near a walk, it may be chemical, as in a spill. One suggestion is dig up the soil and check for whats under there. Its roundish, which may or may not be fungal. Its a small area so digging it up and replacing it is not a hard job, but its a last resort. If you dethach it and seed it, try to do that in the time of year appropriate for that grass, cool season in fall and warm in spring. It may just want some carbon as in humic materials. Folks know the NPK on fertilizer and they know water is H2O but C,O and H are the other three major nutrients and that gets past folks.