While at Ajax, he made his senior Danish national team debut against the Republic of Ireland in May 1978, scoring one goal in the 3–3 draw. Lerby was selected for the Danish national team at the 1984 European Championship, where he played in all four of Denmark's matches, and scored a goal in the semi-final against Spain, which saw Denmark eliminated on penalty shoot-out. At the 1986 FIFA World Cup he played in Denmark's four games, scoring in Denmark's 6–1 win against Uruguay. He was a part of the Danish squad for the 1988 European Championship.