The 1989 Danish 1st Division saw Elstrup score three times in 12 league games, before he left to try his hand at English football.

[1] Playing at Kenilworth Road for two seasons, he soon settled and scored a total of 18 goals to keep Luton up in 1990–91.

Odense only paid £200,000, despite having sold him to Luton only two years before for more than four times that amount, and having attained an impressive goalscoring record at the English club, as well as still being in his twenties.

These strange circumstances were due to damage to body and mind, quote Lars Elstrup himself.

Elstrup made his national team debut in August 1988 against Sweden, and scored both goals in a 2–1 victory.