I was trying to rule out as many causes of the problem you experienced as possible. The reason I asked about whether you left the dough balls uncovered in the refrigerator for a period before stacking was because condensation can form in the stacked metal containers as the dough balls cool down. The condensation can cause the dough balls to become wet and pose a problem when the dough balls are ready to be used. Letting the dough balls cool down before stacking minimizes the condensation problem. With a large number of dough balls, it will usually take longer for all of the dough balls to cool down uniformly and, as a result, it is possible for them to ferment faster and lead to increased extensibility of the dough after a couple of days, especially if held in a home refrigerator. Since you were making only a few dough balls, that shouldn't have been a problem in your case. The fact that your refrigerator or cooler is operating at a proper temperature rules out the possibility of that unit causing or contributing to the problem.
It is definitely possible to make a good NY style pizza dough without using either sugar or oil. Most of the "elite" NY style doughs, such as made at Lombardi's, Totonno's, Patsy's or DiFara's, use no sugar or oil. Sugar is often added to expedite the fermentation process, by promptly feeding the yeast rather than waiting for the enzymes to release sugars from the starches in the flour, which takes some time. The sugar also aids in browning of the finished crust to the extent there are sufficient residual sugars, both natural and added, in the dough at the time of baking to accomplish this result. For those who like a sweet crust, and there are many who do, adding sugar to the dough is the easiest way to get the sweetness. Oil serves multiple purposes, including increasing the extensibility of the dough (by coating the gluten strands), contributing to crust coloration and crust flavor, and helping retain moisture in the dough such that the crumb is soft and somewhat breadlike. The sugar and oil together also act as preservatives by keeping the crust from drying out too fast. This might be a consideration if you are planning to deliver pizzas to your customers. In that case, you could use bread flour rather than high-gluten flour since bread flour will yield a softer crust than the high-gluten flour because of the lower protein and gluten levels.
As you noted, the Lehmann dough formulation calls for only 1% oil. At that level, the effects of the oil are fairly minimal. Many NY styles call for oil in excess of 3-5%, as well as sugar at fairly high levels. These doughs will usually also have a lot more yeast than the Lehmann dough formulation. The finished crusts for those doughs will typically be soft and breadlike and often on the sweet side. The sugar and oil do produce a much more tender crust in this style so it depends on what results you are trying to achieve. The Lehmann dough formulation is more along the lines of the classic NY dough formulations that used only flour, water, yeast and salt and long fermentatation times to allow biochemical development to produce the byproducts of fermentation that lead to good crust flavor, color, odor and texture. I think the use of organic flour complements this process very well.
I think it is a good idea to attempt a dough batch using no sugar. That should extend the fermentation "window" so that the dough won't ferment too fast and be overly extensible when the time comes to shape the dough. I might mention, however, that the Lehmann dough formulation has a natural tendency to yielding doughs that are fairly extensible. It has a high hydration ratio, which itself will cause the dough to ferment faster. That is why it is important to keep the finished dough temperature down and not to use too much yeast, and to get the dough balls into the refrigerator/cooler as fast as possible.