In light of your plans to make a four-day cold fermented Lehmann NY style dough, I thought that you might want to have Tom's view on typical longevities of such doughs. His view was given in response to a poster at the PMQ Think Tank who once asked Tom the following:
Out of curiosity, what is the longest useful life of a cold fermented dough that you have ever seen or heard of, either in a laboratory setting (e.g., at AIB) or in the field? And under normal circumstances, how long can one expect to see a cold fermented dough last and be usable without added sugar to the dough formulation?
The answer that Tom gave was as follows:
Without added sugar 2-days is the norm, and three is pushing it a bit. With 2% added sugar, you can easily go to three days, and with a little luck push it to four. The longest I've seen is 7-days, but the performance of the dough left an awful lot to be desired (finished pizzas over the course of the seven days had everything from a very bubbly edge, to a normal edge, to a knife edge (essentially no rise). The eating texture ranged from tough, chewy to limp and almost soggy....Not exactly what I would want to have representing name or business, but then it wasn't my name or business.
Tom Lehmann/The Dough Doctor