I have a few thoughts that might help you with your Lehmann NY style dough.
First, it looks like you are using one of the early Lehmann dough recipes that called for high hydration at the upper end of the range. More recently, I posted a recipe for a slightly lower hydration percent (63%) that might be a bit easier to use. It is at Reply #86 at http://www.pizzamaking.com/forum/index.php?topic=576.msg7407#msg7407
. You might want to try that version the next time to see if it is an improvement.
Second, you may want to wait until it is absolutely certain that your dough is too wet before adding more flour. My recollection is that you do not have a mixer and are resorting to hand kneading. If you pick up the wet/sticky dough and knead it carefully by hand for a few minutes, even though the dough may seem too wet/sticky and is sticking to your fingers, I think you will discover that the stickiness of the dough will pretty much disappear. If it doesn't, that is the time to add a bit more flour, but only a little.
Third, I think you now know that you have to give the dough a reasonable chance to warm up when it comes out of the refrigerator.
Fourth, from the photo it looks like you used a pan to bake the pizza, rather than a pizza screen or on a pizza stone. I haven't used a pan before with any of the Lehmann dough recipes, but I suspect you will get a more authentic NY style pizza by using a screen or stone. Screens, especially, are quite cheap if you don't have one.
Fifth, I recently posted a message for a new member that pretty much incorporates my thinking on making the Lehmann NY style doughs, including some of the points mentioned above and basic shaping techniques as well. That posting might help you crystallize your own thinking. It is Reply #2 at http://www.pizzamaking.com/forum/index.php/topic,1000.0.html
Feel free to ask any follow-on questions.