I poured straight vinegar onto some ant holes on my lawn. Yes, I now know my grass will die on those parts. Is there any way I can save it?
Dilution will help. Water the patch thoroughly and allow it to spread the acetic acid about a bit, both sideways and down. Yes, the strong acid will have burned some roots; this will result in some leaf death which is kind of inevitable. But then the watering will carry the acid down below the grass root zone which will be in the top few inches. Then the existing soil organisms will rebalance the acidity in the soil back to a neutral state. You could consider adding lime to hasten recovery but the damage is done for now; the burning would be immediate and lasting but only on the finest roots.
The amount of damage the grass will show depends largely on the type of grass. Finer grasses will suffer more, and sturdy grasses like quack grass will have their rootlets burned but will swiftly generate more rootlets from the coarse thick rhizome roots. If you have a good mix of grasses then recovery will not take long.
If any guests ask what happened, explain fully and turn it into a positive learning opportunity.
Further thought: once the area that has been burned shows clearly, if you have a patch of similar grass where you could steal a similar size area you could do what carpenters do to remove unsightly knots by removing the top couple of inches of grass and moving the spare piece in. If you see any landscapers actively sodding in your area, ask them for one or two pieces and offer them coffee in exchange.
I noticed when adding a vinegar solution to some weeds experimentally, only the leaves in the sun were damaged by it. If it's not too late, you can try shading the spots of grass for a while, and diluting it with water as Colin said. I can't say what effect the vinegar would have on the roots, per se.
Vinegar isn't supposed to make soil more acidic in the long run, I've read. So, diluting and shading is probably all that is necessary.