 Lezama was born in Barakaldo, Biscay but moved to England as a refugee at the age of 14.He entered at the port of Southampton on board the "Habana" on 23 May 1937, he and his brother Luis being among 3,889 Basque children fleeing the Spanish Civil War; some of the other refugees also became footballers, including Emilio Aldecoa, Sabino Barinaga and José Gallego.While in Southampton, Lezama played for his school Nazareth House (less than half a mile from The Dell), where he was spotted by Southampton and signed for the club as a trainee, eventually progressing to the reserves before making his first-team debut on 1 June 1940 in a 0–5 away defeat against Arsenal.