First, I haven't watered my lawn in the last week. I don't water my lawn at all, not even in the middle of the summer when it can get really hot and dry. But the last few days haven't been dry or hot. In fact, the first week of June as been really wet and mild. It's probably rained, at least, 4 or 5 days oin the last week. It has also been kinda cold for early summer. Here in North Jersey, it's got down into the 50's a couple of nights last week. It was so cold, a jacket was needed in the morning.
The chilly and wet weather is ideal for cold climate grass such as I have planted in my lawn. If the grass was going to thrive in natural conditions, it would be in weather we've having. You can see that the grass surrounding the strip looks great, and has grown back without any necessary assistance.
If I cut my grass again this week, the shorter grass would only be more damaged. The extra damage would absolutely require you to water it with sprinklers and treat it with fertilizer. This would start the perpetual cycle for your lawn to always need unsustainable management such as extra watering and chemicals.
If you have been mistreating your lawn for years, the length you cut your grass along with how to keep it looking "healthy" only make it harder to get it off toxic chemicals. I think this strip is a great example to show you how it can start. The only way I can get that strip back to health is to let it grow for another week or two before I mow it again.