Maybe yes, maybe no. Need more information.

Where do you live?

What kind of grass do you have?

Maryland, lawn is mix of perennial rye, and tall fescue

Additionally two weeks ago I applied gypsum, and 60 lbs of lime.

Other than what's been applied, obviously I could supplement some iron. I'm just scared that all these applications could burn it. Really trying to get the soil in optimal condition for the fall overseeding

What is the pH level. Looks like that got cut off of the report and is very important. As far as the fertilizer recommendations P and K really shouldn't burn. You could apply half the suggested rate now and then the other half in a month or so. Maybe a little Milorganite to help bring up the iron.

Working under the assumption that the test is right--personally, never count on that--I'd strongly recommend against applying levels of nutrients like those recommended all at once. Particularly since 0-0-60 would be potassium chloride, which is going to be really harsh on a lawn going into summer. Or any time, really.

I'd rather see you use potassium sulfate (0-0-50), but if you already have the 0-0-60, we'll work on it.

This month, you can go ahead and put down 2 pounds per thousand square feet of both the 0-45-0 (triple superphosphate, I'm thinking), and 0-0-60, but no more than that.

I'd skip July and August, and do this again in September at the same time you overseed (I presume you'll water enough to settle this). Then just the potassium in October, you're done with the phosphorus.

Post that, hold off--the soil won't freeze for a while, but P doesn't work in quickly at all. Continue in April with the 0-0-60 at 2 pounds per thousand square feet per month, and the last time in May to complete the 10 pounds.

That also gets you around the issue of it not binding well if you dump it all at once, and the plants will be perfectly happy with a monthly boost during every period where it matters.

Soil ph level is at 5.8, but hoping with the 35.50 lbs at 2960 ft will bump it over 6.0

And thanks morphues