Now, all we need to do is tweak the Lehmann recipe to incorporate an autolyzing step. I'm off to read some more about autolyzing.
Now, to the much tougher question.
Autolyse is a difficult and tricky matter and a subject that is shrouded in much confusion. To begin, the autolyse method involves the simple steps of mixing flour and water together to form a dough and then letting the dough rest for a period of time. The period of rest allows the flour to hydrate more completely. If yeast is added to this mixture at the outset (with a possible exception of a small amount of a natural starter), or if salt is added, the combination is not technically an "autolyse", even though you will find many who incorrectly refer to such as an "autolyse". The original concept of autolyse, which was developed in the context of making European breads, also did not involve adding sugar or oil. Only flour and water. There are many people who, notwithstanding the classic form of autolyse, choose to add yeast and/or salt along with the flour and water, and possibly other ingredients, and then allow that mixture to rest. Is that the same or equivalent to autolyse? Professor Raymond Calvel, who conceived the original autolyse method in the 1970's, would say no. For some of the many reasons for that answer, you might want to read the following thread, http://www.pizzamaking.com/forum/index.php/topic,2632.msg22758.html#msg22758
, and, in particular, Reply 9 in that thread. Arguably, any dough that is subjected to a period of rest will experience some of the effects of a classic autolyse, such as the effects of protease enzymes on the gluten and some improvement in flour hydration, but there are other effects that are outside of the classic autolyse process. But, it is up to you to decide for yourself which methods you prefer.
The duration of the autolyse rest period is also the matter of much discussion and debate. I have seen as little as 5 minutes and up to several hours, and even overnight, for a few dough balls made in a home setting. I would say that the most common rest duration is about 20 minutes to an hour. As I noted in my review of Professor Calvel's book A Taste of Bread
at Reply 9 at http://www.pizzamaking.com/forum/index.php/topic,3220.msg66414.html#msg66414
, Professor Calvel himself used an autolyse rest period of only 13-30 minutes for the dough recipes in his book, and that range was for up to 75 pounds of dough, not an amount of dough for a single loaf of bread or an amount of dough that might be used to make a single or a few pizzas. I think I would use something like 15-20 minutes. But, again, that is up to you.
An additional facet of the autolyse method is how to actually implement the autolyse. When I use the autolyse method, I usually combine all of the formula flour and all of the formula water. I haven't studied all of Professor Calvel's bread dough formulations, but many of them seem to use all of the flour and water in the autolyse (whereas his description of the process talks about autolysing a part of the flour). However, there are others who use various ratios of flour and water for their autolyse, often interspersed with multiple rest periods, apparently with good results. So, that is another area that you are free to experiment with.
With specific reference to the Lehmann NY style dough formulation, I would use the classic autolyse of flour and water and use all of the formula water and formula water and allow the dough to rest for about 15-20 minutes. I would then add the yeast and salt and knead together. The oil can be then be added and kneaded into the dough. Sometimes it can be difficult to mix oil into an already kneaded dough. Fortunately, 1% oil is small enough to combine with relative ease, although if your stand mixer has a C-hook, it may be necessary to help incorporate the oil into the dough by hand.
Using the classic autolyse will allow you to establish an initial benchmark in terms of results. From that point on, you are free to make changes along the lines mentioned above, and as many members have discussed on the forum, and determine whether the changes provide better results from your perspective than the benchmark results. You may even find that you don't like the effects produced on the finished product by using the autolyse method. So, in your case, you may want to try the Lehmann dough without the autolyse and with the autolyse, keeping as many of the variables the same for both tests.