Will more water fix this problem? This brown area was caused by insects – it isn’t for a lack of water, it’s bugs!
If this damage gets worse, this lawn needs an insecticide ASAP but if this is stable damage that has been there for some weeks and not getting worse, insecticide won’t help.
If you find that you need to apply insecticide, you can get one that attaches to your hose and is very inexpensive. Get it at your local hardware store. Brands vary, but you want the one that says “Kills lawn insects” or ‘Kills grubs.”
Don’t expect the lawn to recover from insect damage. Eventually, the dead grass in this spot will all fall out, leaving bare dirt, which will require re-seeding in the fall.