My opinion: the current Lombardi's makes terrific pizza, but it has nothing to do with the restaurant of the same name that served the first U.S. pie.
We never visited the original Lombardi's, but we've been to the current Lombardi's many times. Our first visit was within a couple of days of its opening. The location is down the block from the original. It was said, at the time, to be owned/run, in part, by a descendant of the Lombardi family. The pizza we had that first time was the best pizza we have ever had (it's never been as good on subsequent visits).
I don't remember why - maybe it was because of our enthusiasm - but they invited us back in the kitchen to see the operation and meet the head pizza man, the guy who was supposed to be the Lombardi connection. He was generous with his time, and fascinating to talk with, and he was a brilliant pizza maker to boot. The thing was, as it turned out, except for his pizza-making skills, he was a fraud. There was no Lombardi connection at all, and his well-documented backstory (in all the newspapers of the time) turned out to be fabricated. He was also hiding from all sorts of legal troubles - I forget the details - and I think he soon ended up in jail. In any case, he left Lombardi's, to Lombardi's everlasting detriment. Now, Lombardi's makes very, very good, but not transcendent, pizza.
Bottom line: Lombardi's makes pizza, they have the same name as the old restaurant, they are located down the street from the original, but that's all. They have no connection to the restaurant that first introduced pizza to Americans.