Lavalle attended high school in the United States. In 1984 he won at the side of Mihnea Nastase the junior tournament of the U.S. Open in doubles. The following year, he won at Wimbledon in the individual competition. He was there older than Boris Becker, who won the men's tournament in the same year.
In 1985 he became a professional tennis player, winning in San Luis Potosí his first Challenger tournament. In 1986 he won with Mike Leach for the first time an ATP tournament. After another doubles tournament victory in 1987, he reached in 1988 after victories over other Järryd and Henri Leconte the final of the Cup in Frankfurt, where he was Tim Mayotte inferior. In 1991 he won his only singles title on the ATP World Tour, when he decided as a qualifier tournament of Tel Aviv itself. Overall, he was able to win five doubles titles during his career. Its highest listing in the tennis world ranking he reached position 51 in the singles and in 1992 with position 23 in a double 1986.
His best individual result at a Grand Slam tournament was reaching the second round of the Australian Open 1989. 1991 he reached the U.S. Open the next round, at the French Open semi-final and in Wimbledon finals of the doubles competition, where he of the page Javier Frana was inferior to John Fitzgerald and Anders Järryd.
Lavalle played between 1985 and 1999 38 single and 19 double appearances for the Mexican Davis Cup team. When Erstrundenbegegnung against Germany in 1986 he lost his first match against Boris Becker, but contributed with his victories in a double and single in the decisive match against Michael Westphal to 3-2 win at.
At the 1992 Summer Olympics in Barcelona, he went to Mexico and was eliminated in the quarterfinals against the later silver medalist Jordi Arrese.