Lamza started his career in his hometown Sisak where he played for a local club Segesta and later transferred to a Slovenian club Branik Maribor. It was in Branik when his talent was spotted by, then Yugoslav giants, Dinamo Zagreb and he soon moved there. It was in Zagreb where Lamza made his name and he played a total of 281 games for the blues, scoring 72 goals in the process. He is considered as one of the greatest Croatian football players of all time and a leader of Dinamo's golden generation that won the Inter-Cities Fairs Cup in 1967 and was runner-up four years earlier in 1963. It was in 1967 and the age of only 27 when his career made a dramatic twist as Lamza was involved in an accident that prevented him in reaching football greatness. After the 1967 Inter-Cities Fairs Cup semifinal against Eintracht Frankfurt, when Dinamo managed to overturn their first leg defeat in Germany with a home victory after extra time, he and his teammates went on to celebrate the victory to a luxury restaurant, that lasted late into the night. The next morning Lamza woke up early in the morning in one of the rooms upstairs and found a bar in the lobby below that was empty and started drinking. When other teammates and guest started to woke up they found Lamza drunk in the lobby and one of Dinamo's officials ordered the waitress to take him back to his room so others would not see him in the state he was in. She has done just that and took Lamza to his bed and then locked the door of the room. Later, when Lamza woke up, he was still intoxicated and found the doors locked and went into the balcony where he fell down, hitting the chair with his shoulder and a concrete floor with the right side of his head. He was immediately rushed to a hospital where he stayed for 40 days and was diagnosed with a severe head fracture and most importantly the damage to his nerve center that hurt his center of balance, which subsequently affected his career as Lamza never demonstrated the level of football he did prior to the accident. He followed the final of the 1967 Inter-Cities Fairs Cup by a radio broadcast from a hospital room in Bled. It was this accident that shattered his dreams of playing top football abroad as just after the historic return leg against Eintracht and hours before the accident itself he had immediately signed a contract with Belgian club Standard Liège worth 280,000 dollars, which was a huge amount of money for a player at that time. With his accident and injuries the contract was then never carried out. Lamza returned to football one year later but was not given a chance by the new coach of Dinamo, Ivica Horvat. He made his final appearance for Dinamo on 21 April 1970 on a farewell match, organized by the club, that was played against Benfica and their star player Eusébio. Dinamo won the match 2–0, with Lamza scoring the first goal. Later he had a couple of unsuccessful and short lived spells at clubs home and abroad, but never fully demonstrated the level of football he did prior to the accident. He returned to football at the beginning of the nineties as a Dinamo's scout.
International career
Lamza has made a total of seven appearances for Yugoslavia national team. The reason for so few caps being the accident and the supposed discrimination of Dinamo's players at the time.
Personal life
Lamza once stated that he was probably saved when Dinamo's patronageZdravko Mamić and head coach at the time Miroslav Blažević offered him to work for the club, at the beginning of the nineties, as he had only around 200 euros of pension from which he does not know how would he been able to survive. He also stated that he sees Luka Modrić as his successor due to his similar style of playing and physique.