Moore was both a great runner and receiver. He lined up both in the backfield as a halfback and split wide as a flanker, and was equally dangerous at both positions in the offense engineered by quarterback Johnny Unitas. Moore averaged at least 7.0 yards a carry in several seasons. He made 40 receptions for 687 yards and seven touchdowns in 1957, the first of five straight years in which he would have 40 or more catches. In 1958, he caught a career-high 50 passes for 938 yards and seven touchdowns in helping the Colts win the NFL championship. Then in 1959, Moore had 47 receptions for 846 yards and six TDs as the Colts repeated as champions.
Moore was tagged with a number of nicknames: "Sputnik," for the fear he incited in opposing defenses; "The Reading Rambler" and "Lightning Lenny," for his unmatched speed; and "Spats," for the way he taped his high-top shoes, making them look like low-tops.
After being injured in the 1962 season and losing his starting job, Moore had one of his best statistical seasons in 1964 when he scored 20 touchdowns, and helped lead the Colts to a 12-2 regular-season record and a trip to the NFL championship game for the third time in seven seasons.
Moore scored a touchdown in an NFL-record 18 consecutive appearances starting in 1963 and continuing through the entire 1964 season, ending in 1965. This record stood for 40 years until being equaled by LaDainian Tomlinson in 2005. Because his streak was interrupted by a five-game absence due to injury in 1963, he does not hold the NFL's official record for consecutive games rushing for a touchdown.
Moore occasionally speaks to student groups about his experiences as a black football player during an era when, in the words of Baltimore Sun sportswriter Rick Maese, "Moore could travel with his teammates but couldn't always eat in the same restaurant, couldn't always stay at the same hotel, couldn't always fraternize with them the same way out of the locker room as he had in it."
"There was never anybody ever closer than me and the guys that I played football with on that Baltimore team-- on the field," Moore told the Sun. "We were just like glue. One for all, all for one." But "once they blew the whistle and the game was over, they (the white players) went their way, we (the black players) went our way. We split. It was race."
Teammate Ollie Matson mentored Moore and warned him that "'they're going to call you the big N. You're going to hear it all. So don't get yourself all worked up, because it's going to happen.'"
Moore retired after the 1967 season. His uniform number 24 was retired by Baltimore, and in 1969 a sportswriters' poll named him to the NFL's 50th Anniversary Team. In 1975, he was elected to the Pro Football Hall of Fame. In 1999, Moore was ranked number 71 on The Sporting News' list of the 100 Greatest Football Players. He is also the only player to have at least 40 receiving touchdowns and 40 rushing touchdowns. Football Outsiders, in their book Pro Football Prospectus 2007, named 6 of his seasons among the top 500 running back seasons of all time, which was tied for the 5th most seasons among the top 500 of any player. Moore's retired number is honored along with all of the other Baltimore Colts retired numbers in M&T Bank Stadium in Baltimore, home of the Baltimore Ravens.
Moore was an honorary captain for Penn State's game versus Syracuse on September 12, 2009. It was the first time a former Penn State player has been invited to participate in the pre-game coin toss.