He won a goal medal in football at the 1968 Summer Olympics and a silver medal in football at the 1972 Summer Olympics, and also participated in UEFA Euro 1972. He earned 33 caps and scored 7 goals for the Hungary national football team. He started his career in his native town of Szeged, with third-division Szegedi VSE. Lajos became a first-division player in 1966, having been transferred to then first division Salgótarjáni BTC. A year later, he moved to Budapest to play for Honvéd, where he spent ten years and became one of Hungary's best-known and most popular football players. Kocsis was considered as Hungary's most talented footballer since Ferenc Puskás, some stating he was even more talented than his famour predecessor. Yet he failed to fulfil the expectations of both fans and experts because of his flamboyant lifestyle (including frequent and hard drinking), which ultimately led to his expulsion from Honvéd in 1977, despite having been one of the most popular characters in Hungarian football, adored both for his high technical skills and good sense of humor. He was particularly feared by his adversaries for his free-kicks and unpredictable, Garrincha-type dribbling. He scored one of his most memorable goals at Vienna's Prater Stadium in a 1974 World Cup qualification match against Austria on 15 October 1972. Following the end of his stay at Honvéd, he played for second-division Gyulai SE. During the last years of his life, while working as a gastronomer and coach of lower division teams, he suffered from health problems that led to his death. He was known to his fans also by his nicknames "Kicsi" (tiny) and "Csikó" (foal), because of his short height. His son Lajos Kocsis Jr. was also a football player but had a much less outstanding career, mostly playing for lower division teams.