You say the customer wants a "wants a 3” NPT tapped hole." in a blind hole. First, this sounds like a glue fitting so I have to ask is that hole even deep enough to allow a proper, full length thread to be cut? A threaded flange would be engineered long enough to take care of this problem, but if this is a glue flange, then it may not be. You may only have enough length for a partial thread and, with a blind hole, the pipe may not fully seat in whatever thread you can cut. Heck, you may not even have a proper diameter hole for a 3" NPT thread as a glue fitting will have a hole with a diameter slightly larger than the OD of that size PVC pipe while a thread would be cut DOWN into that OD. If this needs to be liquid tight, they may have problems. Even if it is for some kind of handrail or support, it could make a loose joint and therefore be dangerous. If I were asked to do this, I would want to have the mating part on hand to ensure a proper fit. And may have more questions after that.
Pipe threads are tapered so I am not completely sure how you can do that on a lathe. I would assume it could be done with a taper attachment.
Personally, if I just had to thread this flange, I would try using a tap. It is a blind hole so a standard tap may be too long. A 3" tap will be expensive and cutting one down may be a losing proposition if it does not work. I have had good luck making a pipe thread tap from a length of galvanized pipe or a pipe fitting. I just filed some notches at the correct angle to provide a rake angle and I screwed it into a proper sized hole in the PVC part. That works just fine for one or a few parts and saves the cost of what could be an expensive tap. These filed "flutes" will be small so it must be backed out several times during the tapping process to clear the chips. The taper of the thread takes care of any tolerance issues involved as a pipe thread is tightened until it is liquid tight.
Frankly, to me this sounds like an nu-knowledgable person (the customer) who is trying to do something the wrong way. They do make PVC fittings with threads. It may take an order from someone like McMaster to get some in this size, but that would be the best way to do this as a proper fit would be ensured. It may take a phone call to their sales force as it may not be found in the catalog or on their web site. They do have people who can help with things like this.