It’s difficult to “transplant” people from one era to another and predict success or failure. This is particularly true of athletes because over time they have become bigger, stronger, and faster. But when evaluating a coach that concern is replaced with another: Could he adapt to the current era? Certainly if Vince were still alive, at age 100 he wouldn’t be physically able to coach so the question asked in this thread presupposes Vince’s date of birth be moved forward by several decades. Unless we suppose he was born later but still retained memories of a previous life we have to assume he would be fully aware of the surroundings in which he grew up and worked. In other words, in Vince’s case that means he would be fully aware of the changes in culture and society as well as the changes in football strategy.
So if Lombardi were in his 40s or 50s today, would he be a successful coach? No one can answer such a hypothetical with facts but my answer is an absolute ‘yes’. Lombardi was a great coach and leader regardless of the sport. For example, after being hired as a teacher and football coach at St. Cecelia High School, he was offered the job of coaching the basketball team. According to more than one source, Lombardi had never coached or even played basketball so he read some books on the subject. His winning percentage in basketball at the high school was about 65% and he led the team to a state championship.
IMO Lombardi was a master psychologist and that was his greatest attribute as HC. Culture and attitudes change but the fundamentals of human psychology do not; they transcend eras. Lombardi was also a master teacher and his main subject matter was fundamentals. Of course that means blocking and tackling in football and whether it's Pop Warner’s single wing or some version of the WCO in vogue, blocking and tackling remain fundamental to winning football. Another of his attributes transcends time: Lombardi had an attribute shared by nearly all great leaders in history: He was charismatic.
If Lombardi were born one half century or so later if given the opportunity, could he pick up a book or two on football strategy and immediately lead an NFL team to five championships in nine years? Probably not, but I think he’d get there eventually. In fact if his career path approximated his actual one, he probably would get there more quickly than he actually did because he believed (and I think it’s reasonable to assume) his ascension through the coaching ranks was delayed because of prejudice against his Italian heritage which likely wouldn’t have held him back in a more “modern” era.
While I'm in general agreement with your approach to the question, I'm afraid if he were 40 or 50 today I doubt he'd have ever gotten close to a pro head coaching job for the simple reason he would have been too small to play college football and would not have even gotten off the bench at a lot of high schools. By some reports, he was about 5'8" and played OG at Fordham at about 180 lbs. Not playing in college would be a career path killer.
That consideration aside, I agree that in terms of temperament, intelligence, work ethic, adaptability, character and the ability to "see" into the game...would have made him an outstanding coach in today's game.
The idea that Lombardi's temperament would not have meshed with today's players doesn't hold much water in my mind. Beside the points you noted regarding his skills as a psychologist, I would comment that Parcels and Coughlin, to name two off the top of my head, were/are crusty, demanding disciplinarians who don't suffer fools well. They've had a little success, I think, in the free agent/high pay era.
On the point of adaptability, it is helpful to note that the difference between the game Lombardi played at Fordham in the 1930's and the one he left in 1969 is greater than the difference between the 1969 pro game and the one we see today. If you dropped him down out of heaven today, gave him a rule book, and a thousand hours of tape, he'd have it pretty well figured out. During one of the Lombardi documentaries they've been showing on NFL Network this week, one of his ex-players commented that on his death bed Lombardi was thinking about how to attack the 3-4 defenses coming out of the AFL. Something tells me Lombardi would not be caught off guard by a pistol read-option offense after the requisite amount of study.