Fertilizer is important. But, the time of fertilizing is just as important. Ground should be given food when it can use it. If 2 lbs of fertilizer per 1000 square feet is the required amount, then putting down 4 lbs is not the thing to do. Too much fertilizer causes all kinds of problems which you can read about by doing research on the subject--when to fertilizer.

Plants use fertilizer when they are actively growing....so that means spring/summer/fall.
A regular schedule of a fertilizer program is one way to ensure the lawn receives adequate food. The type of fertilizer depends on the type of grass you have and the amount is easily discerned by dividing the 1st number (nitrogen) into 100.
Thus a bag that is 24/6/12...24 nitrogen, 6 phosphurus and 12 potash (potassium) is recommending that 4 lbs per 1000 square feed be given of that material. 100 divided by 24.
This is usually spread in a north/south direction half the amount, then in a east/west direction the other half of the amount.
A forty pound bag of fertilizer in this case would inform the buyer he will obtain 40 divided by 4 lbs = 10 X 1000 square feet....= 10,000 square feet of coverage for that bag.
Keep lawn fertilizer away from flowering plants--the high dose of nitrogen could cause the flowering to be cut or even prevented. Nitrogen does that, causes great growing of green, but tells the plant to do that instead of making bloom. For areas next to garden plots, hand spread the fertilizer.
One of the most popular garden fertilizers on the market is "Miracle Gro"...it has a ratio of elements 15/30/15
the '30' is the amount of phosphurus which aids in flowering.

Kentucky Bluegrass is one of the most put down types of sod for northern areas--its a cool season grass that takes well the heat of summer and average amounts of moisture.
You might look into overseeding areas instead of laying sod over the entire area and a combo of Bluegrass/perennial ryegrass and fescue can help a lawn stand up to most conditions including drought and heat of summer.