From 1959 to 1964, Lary was the most dominant punter in the NFL. He led the league in punting average in 1959 (45 punts for a 47.1 yard average and a long punt of 67 yards), 1961 (52 punts for an average of 48.4 yards and long punt of 71 yards) and 1963 (35 punts for an average of 48.9 yards and a long punt of 73 yards). Lary narrowly missed a fourth punting title in 1964, trailing Bobby Walden by one-tenth of a yard (or 3.6 inches) at 46.3 yards per punt. In 1962, he was two-tenths of a yard from the lead, losing the punting title due to a single blocked punt. Over the course of his 11-year NFL career, he punted 503 times for 22,279 yards for an average of 44.3 yards. His 48.9 yard average in 1963 was the second highest single-season total in NFL history, trailing only Sammy Baugh's 51.3 yard average in 1940. At the time of his retirement in 1964, Lary's 44.3 yard career punting average ranked second in NFL history, trailing only Sammy Baugh.