Jensen attended the University of Southern California and was a professional tennis player in 1987. He was specialized in the double game, and played for several years with his brother Murphy. He was at the ATP World Tour win ten tournaments in doubles competition, another 14 times he stood in a double finals. Its highest listing in the tennis world ranking he reached in 1988 with position 168 in single and in 1993 with position 6 in doubles.
His best individual result at a Grand Slam tournament was reaching the second round of the U.S. Open in 1985 and 1986. In doubles, he won at the side of his brother Murphy at the French Open in 1993 against the German duo of Marc -Kevin Goellner and David Prinosil. Jensen was one of the few two-handed player on the ATP World Tour, he could change the game hand during a match. Hence his nickname Dual Hand Luke resulted.
In 2006, he became head coach at Syracuse University.