As a member of the Spanish national team, Luyk won a silver medal in the EuroBasket 1973 with the Spanish national team. He also played at the 1968 Summer Olympic Games, EuroBasket 1969, EuroBasket 1971, the 1972 Summer Olympics, EuroBasket 1973, the 1974 FIBA World Championship, EuroBasket 1975, and the 1975 Mediterranean Games.