Lőrinc Galgóczi (born as Geiszler) began his sports career as an athlete of MAFC. He later became acquainted with basketball and handball within the association, so much so that the latter also took over the leadership of the department. In basketball he won the bronze medal at the World College Games in Budapest in 1935.
As a handball player, he was contracted to the Újpest team, where he won the championship in 1936 and 1938. Between 1933 and 1939 he appeared in the Hungarian national team nine times. Out of these, four games were at the 1936 Olympics, where he was a member of the fourth-placed team.
After completing his sports career, he worked as an engineer.