Do not add lime. You do not need phosphorus. What you need, besides nitrogen, is potassium. Logan is saying the deficit is 193 lb/ac in the front and 154 lb/ac in the back. Dividing those numbers by 43.56 to get lb/1000 square ft, the shortage is 4.4 lb/K and 3.5 lb/K. However, if you use the SLAN method, you convert lb/ac to ppm and the "value found" would be 44 ppm for the front, 43 ppm for the back (at 6 inches of reported depth, lb/ac = 2 x ppm). SLAN sufficiency level is greater than 110 ppm. So the shortage is 66 ppm and 67 ppm. Converting that to lb/ac and then to lb/K, the shortage is 3 lb/K. So, you need some potassium. You can go with Logan's calculated shortage or the SLAN calculated shortage. Do not add more than 1 lb/K of K20 at an application (that would be the K number in NPK--I'm using K here two different ways. lb/K refers to pounds per 1000 square feet, K as in NPK is potash). You could use a fertilizer with close numbers for N and K and no P. Or you could use potassium sulfate (O-0-50) with a fertilizer that is mostly N. That would give you some flexibility in when you apply K (you could do them separately or together). For cool season grass, the usual times to apply nitrogen are late May and then in the fall (number of times depends on what kind of grass), avoiding the summer. If you have prolonged snow cover in the winter, don't apply K past September. You can apply some this year, some next year. Just make sure you get some down. And make sure to water in any synthetic fertilizer right after applying it. The shortage, 3 or 3.5 and 4.4, is shortages of potassium, the plain element. It only comes in K2O form so you multiply by 1.2 to get shortages of potash (the K in the NPK numbers, which is actually K2O). So you would aim for 3.6 lb/K or 4.2 and 5.3 lb/K of potash in the course of amending your soil.

Suffolk County prohibits fertilizer between Nov. and April. See link If you're not in Suffolk, your locality may have restrictions.

Pretty nice soil.

Stay away from any sources of P. I'm surprised Becky didn't give you a mycorrhizal fungi talking to.

Don't apply more than 1#k (1.2# of K2O/k) of K at any one time, nor more often than 4 weeks of one another.