...My lawn is a bit dried out/cooked at the moment from no measurable precipitation in 3 weeks...... I haven't fertilized the lawn in the 9 years I have owned the property. There are weeks that I need to mow twice a week the grass grows so fast.. I can't imagine what it would be like if I put down any fertilizer. My soil does have a high clay content.
I'm going to go out on a limb to challenge what I believe are common myths, and hope to draw out support or challenge to my suggestions.
I'd bet the OP doesn't mow twice/week during a dry spell, and my own contention is that it's
water that stimulates growing height above all else.
Fertilizer, like mowing 'tall', will improve a lawn's o'all
health and, by leaving longer blades to 'feed' on sunlight, will grow thicker as well as shading the lawn against evaporation. When I spill fertilizer (ten thumbs method

), the bit surrounding what's 'burned' by too much is greener and thicker more than that much taller than the rest of the area.
While many clay-rich soils are alkaline, and while gypsum is often used to lower PH and 'loosen' them, some are acidic ... something that strawberries thrive on. What the OP & I have in common is PH(?) & geographical latitude, and the ~1 1/2 ac that I mow has evolved under a decade of my care. I spot spray to control weeds and while progress has been slow-ish it's been steady. Strawberries too widespread to treat seem to gradually diminish as the grass fills in and crowds them out.
IXLR8, would you consider treating a small area as I do to see if the benefits outweigh the extra effort? btw: be assured that I 'feed' as sparingly as I spray, usually at 1/4 the recommended amt/area, but in my case
some has been much better than
none.
Rebuttal, anyone?