I have set forth below the formulations for the 50- and 25-lb. versions of the Lehmann NY style dough. You will note that the 25-lb. version is simply half of the 50-lb. version.
For purposes of crunching the numbers, I have assumed the use of high-gluten flour. The same numbers should also work reasonably well for bread flour, especially if you use the King Arthur brand of bread flour which has a higher protein content than most competing brands. I have also supplemented bread flour with vital wheat gluten before and gotten good results. If you choose to go that route, I would recommend coming up with a formulation just for that application. I would not recommend using all-purpose flour. In my opinion, it does not work nearly as well as high-gluten flour or bread flour, even if supplemented by vital wheat gluten. That said, however, I have managed to come up with a combination of all-purpose flour, vital wheat gluten and dried dairy whey that produced the best all-purpose version of the Lehmann NY style dough of the many I tried. If you get to the point where you feel you have to use all-purpose flour, let me know and we can consider what might be the best approach for you.
Here are the two formulations you requested:
50-lb. Version of Lehmann NY Style Dough
100%, High-gluten flour, 50 lb.
63%, Water, 31.5 lb.
1.75%, Salt, 0.875 lb. (14 oz.), 1.48 c.
0.25%, Instant dry yeast (IDY), 0.125 lb. (2 oz.), 6.27 T.
1%, Oil, 0.5 lb. (8 oz.), 1.01 c.
Total dough weight = 83 lb.
25-lb. Version of Lehmann NY Style Dough
100%, High-gluten flour, 25 lb.
63%, Water, 15.75 lb.
1.75%, Salt, 0.4375 lb. (7 oz.), 11.85 T. (about 3/4 c.)
0.25%, Instant dry yeast (IDY), 0.0625 lb. (1 oz.), 3.14 T.
1%, Oil, 0.25 lb. (4 oz.), 8.10 T. (a bit over 1/2 c.)
Total dough weight = 41.50 lb.
You didn't indicate what size pizza(s) you plan to make. This is not a problem, and you can use the quantities of dough calculated above to make any size pizzas you want. However, you will want to make the right amount of dough for each pizza size. The way to do this is to use the following expression:
DW (dough ball weight) = 3.14 x R x R x TF,
where R is the radius of the pizza and TF is the thickness factor. For our purposes, I would use a value of 0.105 for the thickness factor. So, for example, if you want to make 12" pizzas, the value for DW above would be equal to 3.14 x 6 x 6 x 0.105, or 11.87 ounces. On this basis, the 50-lb. formulation would be enough for you to make around 112 12" pizzas (83 lb. x 16 oz./11.87 oz. = 112) The 25-lb. version would, of course, make half that many, or 56 pizzas. If you would like to make an even thinner version of the Lehmann NY style, you could use a thickness factor of 0.10 in the above expression, and get a handful more pizzas out of the process.
The Lehmann formulation is intended for a cold-fermented dough. It is possible to use a room-temperature fermentation for whatever dough you choose to use, but it will be necessary to strike the right balance between the flour used, finished dough temperature, room temperature, amount of yeast used, and time. Dough temperature is a function of flour temperature, room temperature, water temperature, and the frictional heat contribution of whatever machine you use to make the dough. It is possible to adjust water temperature to get the proper finished dough temperature (around 75-80 degrees F) and compensate for all of the other temperature components mentioned, but it is tough to calculate how much yeast you will need in order to have the dough ferment at room temperature and be in proper form at the precise time you plan to use it. The most logical way to do this would be to use less yeast than called for in the formulation and use cooler water. Unfortunately I don't have any formula or expression to calculate these sorts of things by plugging in all the variables. You would have to make a few dough balls and see how they turn out over the timeframe you have in mind. As noted above, the answer will also depend on the particular flour used. All else being equal, high-protein/gluten flour will tolerate longer fermentation times than lower-protein/gluten flours.