Lourdes Góngora began playing tennis at a young age at a local club in Mexico City. Góngora competed at multiple tournaments during the late 1960s and early 1970s, winning a handful of minor singles and doubles titles. In 1967 she played in the first round of the French Open but lost in straight sets to Annette Van Zyl of South Africa. One year later she competed at her home Olympics in Mexico where tennis was a demonstration sport, including doubles and mixed doubles events with Patricia Montaño and Vicente Zarazúa, respectively. By 1971 Góngora was forced to retire from the sport due to a long-standing shoulder injury.