Lassiter was born in Washington, D.C., but grew up in Raleigh, North Carolina where he attended Athens Drive High School. He was the North Carolina State 4-A Player of the Year as a senior and a high school All-American. That year, he led his high school soccer team to the state championship while scoring a state record 47 goals. He also played for a local youth club, Raleigh United, which lost to the LaJolla Nomads in the 1989 McGuire National Club Championship Cup. Lassiter attended Lees-McRae College in 1989. He then transferred to North Carolina State University where he was a 1991 First Team All-ACC and All South.
While convalesing, Lassiter was contacted by Turrialba from Costa Rica in 1992. As Lassiter recalls it, "I have no idea how they got my name. They paid for my trip down there while still recovering from my leg injury, and I signed a contract." He also played for Carmelita and in summer 1995, Alajuelense sold him to Major League Soccer.
Lassiter was called up to the U.S. national team in January 1992. He earned his first cap as a substitute for Eric Wynalda in a 1-0 loss to the Commonwealth of Independent States which briefly succeeded the Soviet Union. However, he broke his leg in a practice collision with Bruce Murray a few days later. That year he also earned his second cap with the national team when he came in as a sub for Frank Klopas in an August 16 loss to Sweden. Two months later, he played a third time for the national team, again as a substitute, this time for Roy Wegerle. Lassiter scored the game-winning goal in a 4-3 victory over Saudi Arabia. Lassiter's career continued to rise, he earned his first start for the national team in December 1996 and became a regular for much of 1997. While Lassiter had played consistently for the U.S. in 1997 his appearances tapered off in 1998 and he was selected as an alternate for the 1998 FIFA World Cup roster. He played only one game in 2000, his last with the national team. He represented his country in 4 FIFA World Cup qualification matches and finished his international career with 30 caps and 4 goals.