"Grant says Tiger Mothers and Lombardi Dads often focus on achievements because they're easy to measure."
I never heard of this expression before, but I did some research on it and think I have the answer.
According to this Wikipedia article, Vince Lombardi was a famed football coach with a high sense of "perfectionism, authoritarian nature, and temper". In his role as a father, he would fit your idiom perfectly. According to this fan page, "he conducted grueling training camps and demanded absolute dedication and effort from his players".
The coup de grâce: In an interview here, Lombardi's son, Vince Lombardi Jr., described his father as having "not so great qualities for a father from the standpoint of his only son".
The expression doesn't appear to be common, however. Google NGrams has no results for any variations of "lombardi dad", and Google Trends show searches for the topic below one hundred per month. It might even have been made up on the spot; the author of your article was once described here as "too weak for football", showing that he at least had an interest in the sport, and according to here he once taught a seminar in April 2012 titled National Football League “Motivation and engagement”. Perhaps the author was just struck by a whimsical desire to display his football knowledge, and perhaps not. It does, however, seem self-evident that the term referred to Vince Lombardi.
"Winning isn’t everything; it’s the only thing" [...] is widely, but wrongly attributed to American football coach Vince Lombardi.