I think adding lime is a good idea. It will allow more nutrients to be available. The drawback with soil savvy is this is a picture in time of available nutrients at this ph. Once you lime and raise it to 6.5-6.8, more nutrients will be available so you will need to retest. Lime takes time to work and core aerating can help get the lime lower into the soil. Lime doesn't move quickly through the soil. It can take 6-12 months to move down through the soil. This can be a drawback to using soil savvy since you don't know the whole amount of nutrients in the soil, only what is currently plant available. Also, since soil savvy doesn't give a CEC number, I wouldn't know what to recommend for the quantity of lime. If you have an idea of your soil composition, ie more clay, more silt, more sand, you can ball park the amount of lime and retest in a year to see the difference. Sand maybe 10 lbs/M, silt maybe 50 lbs/M, clay maybe 100 lbs/M. As a note, it is easier to raise than lower the ph so, perhaps, be conservative on the quantity. Also, if you don't core aerate before and you get a heavy downpour, you may lose a lot of your lime through runoff.
In the meantime, I agree with g-man. A balanced fert looks fine or even go low on P and use something like a 20-10-20. If that isn't available, you can use regular 29-0-10 and add SOP or MOP to it. If you don't get much rain, go with SOP due to the lower salt index.