In the basic Lehmann NY style dough formulation, including the versions posted earlier in this thread by both Art and me, the oil is mandatory but the sugar is optional.
Not too long ago, I asked Tom Lehmann about the use of sugar and oil in his NY style dough formulation and his answer is quoted in Reply 7 at http://www.pizzamaking.com/forum/index.php/topic,7489.msg64438.html#msg64438
. As noted in that reply, it is possible to omit the oil, as is frequently done by pizza operators for certain NY style doughs. Although not mentioned in Tom's reply, oil also helps to improve the rheology (flow characteristics) of the dough by coating the strands of gluten. This improves the extensibility of the dough.
Tom Lehmann usually only specifies sugar in his NY style dough formutation when the dough is to be held beyond a couple or few days. That is to make sure that the yeast is adequately fed over that time period and that there is sufficient residual sugar in the dough at the time of baking to contribute to crust coloration. However, if the pizza is baked before about two days, the sugar in the dough at that stage can lead to premature browning, or even burning, of the bottom crust when the pizza is baked on a very hot surface, such as the stone surface of a deck oven. Also, there may be a deeper crust coloration overall because of the higher levels of sugar at this stage because the yeast hasn't yet consumed a good part of that sugar. If you would like to see an example of this phenomenon, look at Reply 45 at http://www.pizzamaking.com/forum/index.php/topic,6758.msg63672.html#msg63672
. In that example, the dough (a Peter Reinhart American style dough) had a lot of sugar added to it (about 5.6%) together with a lot of milk, which includes lactose. Lactose is unique in that it is a milk sugar that is not used as food by the yeast yet contributes to crust coloration. Because of the very high sugar levels in that dough, I had to bake it on a pizza screen.
With all the above said, it has been my experience that using 1-2% sugar in a Lehmann dough to be baked in a standard home oven on a pizza stone is not likely to result in premature browning or burning of the bottom crust. My recollection is that Tom himself has said pretty much the same thing, as I noted at Reply 26 at http://www.pizzamaking.com/forum/index.php/topic,2797.msg28607/topicseen.html#msg28607
Your quoted "tidbit" about sugar is correct but to get a sweeter, more moist crust, you will usually have to use more than 1-2% sugar and there has to be enough total sugar in the dough unconsumed by the yeast at the time of baking to be able to taste it. When I did all my experiments with the Papa John's clone doughs, I used around 4% sugar. At that level, I could taste it in most cases. Different people have different sensitivities to sugar, so that is a factor to take into account.
In re-reading your post at Reply 27 at http://www.pizzamaking.com/forum/index.php/topic,7530.msg65287.html#msg65287
, you posed a question about getting more "tang" in the finished crust. There are many ways of achieving this result but you would have to reformulate the basic Lehmann dough formulation and dough preparation and management instructions. An example would be to use a preferment approach, such as a poolish, or a starter culture as you mentioned. Another way would be to use a very long room temperature fermentation, such as discussed at http://www.pizzamaking.com/forum/index.php/topic,7225.msg62332.html#msg62332
. In that method, the yeast would have to be increased from the stated amount because of the cooler weather this time of year.