Nico - I've reviewed your soil test results, I see that your pH is 7.7, the Potassium is Below Optimum and the organic matter in the soil is 1.3%.

Addressing these three findings:

*  You can apply elemental sulfur to lower the pH and according to the chart in the link below, with clay soil you would probably need to apply more than 5 lbs. per 1,000 sq. ft.  Per the article, "most urban soils require between 35-56 lbs./1,000 sq. ft to lower soil pH 0.5 units".  With the recommendation to "not apply more than 20 lbs. of sulfur/1,000 sq. ft. at any one time, you could apply 10 lbs. in the first application and then another 10 lbs. later in the year.  The second article below provides somewhat the same view with the caution that the reduction of pH may be transitory so keeping the pH at a lower level may be the challenge.

https://uwlab.webhosting.cals.wisc.edu/wp-content/uploads/sites/17/2010/12/lowering_ph.pdf

https://www.canr.msu.edu/news/reducing_soil_ph_in_landscapes

*  That being said, if you increase the organic matter in the soil, it should will help lower the pH over time.  Incorporating organic matter will gradually lower the pH over time by as they decompose and release acids.  I am including a link below with a variety of information about smart gardening with soils and composting.

https://www.canr.msu.edu/home_gardening/soils-compost/

*  Below Optimum Potassium:   Potassium does not generally affect the pH of the soil but by increasing the organic matter in the soil, this will affect the Potassium.  Organic matter influences the retention, release and uptake of the Potassium

The recommended fertilizer ratio in your soil test results is 1:0:1 or 1:0:5 which would provide Nitrogen and Potassium in a balanced fertilizer.  These ratios are general guidelines so if you cannot find a product with this ratio (i.e. 12-0-12) then select one that has both nutrients.  Come back to the MSU soil test site and enter the nutrient numbers into the Fertilizer Calculator (found under Tools) and the site will calculate how much of that product to apply over 1,000 sq. ft.  per year.  With 7500 sq. ft, you will need to multiply that amount by 7.5. Follow the application recommendations on the product and apply throughout the year when turf is growing (i.e. not dormant). 

In addition, you may want to apply a separate Potash fertilizer (usually found in garden centers or larger quantities at farm mills).  Typically the potash fertilizers come in 0-0-52, 0-0-60, or 0-0-62.  The higher the Potassium number, the lower amount you would need to apply.  Again, once you have selected the product, you will want to use the Fertilizer Calculator to determine how much of that product to apply in one year over 1,000 sq. ft.  Don't apply at the same time as the balanced fertilizer and it is usually recommended you don't apply more than 1 lb. at a time so the lawn is not burned.

Good job starting with a soil test to know the health of your soil.  Hope that helps!