Question
QUESTION: If one is not supposed to fertilize cool season grass lawns, what is one to do at the end of June when the lawn is browning out and in need of a boost?

ANSWER: Irrigate.
Though some soil structures do not retain moisture well, water is likely the tonic needed.  The amount must be tailored to your soil and turf response.  One acre inch is recommended.  More may be required.  Scale this out over a week or do it regularly each week.
Fertilizer at this point may cause more burning.  Without water to feed growth, the salts of fertilizer will further burn the grass plants.
Some Milorganite or other slow release organic applied at .5 lbs/1000 sq ft. could help, but I would depend on preparations done last spring and fall for feeding and seeding.  Wait until fall to feed again.


---------- FOLLOW-UP ----------

QUESTION: Thanks for your reply!!!
Do you think it would be helpful to aerate, as well?
What are the signs that a lawn's soil needs aeration?
Thanks, again!

Answer
Absolutely!
Aerate after watering though.  In dry weather, aeration is like driving nails into bricks.
I use a very scientific measurement for need of aeration:
If I can walk comfortably on the lawn and feel give in the soil, it is all right.  If it is hard and uneven, with bare spots and weak grass, I aerate with each overseeding until it passes the test.  Combine all that with topdressings of compost in fall or spring.
Best of luck.