You need to do and exploratory dig to figure it out for yourself. That is, carefully remove enough of the overlying soil to assess where the roots are and, hence, answer your question in a semi-quantitative way. Generally, landscape trees don't get watered near the trunk. Therefore the fine 'feeder' roots will be just beyond the edge of the canopy, in the area of the 'drip line' as its called. On the other hand, if your neighbor irrigates this tree, there may be lots of 'feeder roots' close to the trunk and the root ball you would need to lift would be considerably smaller.
Further, you need to assess what kind of soil the roots are in. If it is sandy loam, you might be able to dig around and under virtually all the roots, lift the tree and shake out the dirt, and leave with your tree in one-hand, carrying it over to your place to pot up. On the other hand, if it is heavy clay, you will likely need an engine hoist, a BobCat, or a crane to move it.
Since you convinced your neighbor to wait until fall, you could also cut the longer roots closer to the trunk now. If all of them are long, only cut about half of them, but evenly around the tree. Dig a little trench where you cut and remove the bits and then simply fill it back in. The cut ends should develop 'feeders' so that come fall, you cut the remaining long ones at the same distance and lift a tree with a much smaller root ball. I suggest that you do this now, and irrigate the cut areas during the summer. There is no guarantee that it will produce enough adventitious roots to make a harvestable air layer.