Can you give us an idea of what size pizzas your new Pizza Alfredo pizza maker can make, or that you plan to make? Also, do you have access to the Caputo brand of 00 flour and, if so, which specific one (in the U.S., there are three Caputo 00 flours used to make pizza).
The Lehmann dough formulation is intended to be used with a high-gluten flour, or at least a bread flour. You can perhaps substitute a 00 flour such as the Caputo 00 Pizzeria flour but its rated absorption is around 57%, whereas for high-gluten and bread flour it is in the range of 61-63%. It is possible to use a hydration for the 00 flour that is above 57%, but unless you have had experience working with fairly wet doughs it may take a while to master the process. But even if you are able to do that, what you are likely to end up with will be more like a Neapolitan style dough rather than a NY style dough. To make a classic NY style dough, you would want to use a high-gluten flour or a bread flour. Such flours have higher protein contents than 00 flour. For example, bread flour has a protein content of about 12.7% and high-gluten flour has a protein content of around 14.2%. By contrast, the Caputo 00 Pizzeria flour has a protein content of 11.5-12.5%. It is also common, but not necessarily mandatory, to use a bit of oil with a NY style dough, and sometimes some sugar. Classic Neapolitan style doughs use no oil or sugar. What you really want with a Neapolitan style pizza is very high oven heat. Whether your new pizza maker can provide the right type of high heat is an open question, at least for me.
Once you provide the information requested above, maybe we can come up with a 00 dough formulation for you to use to test drive your new pizza maker.