Lygaard joined from Konami, the Japanese video game manufacturer, in the summer, as did Joe Manns, as Head of Recruitment and Player Development.
Since then the focus has returned to finding a successor to Haysen, with familiarity with Danish football considered essential.
Lygaard continued: "It is important for us to get a Danish sporting director in, and that is not really something I want to compromise on. He must also have knowledge of football, but the Danish part has been a really important thing for me.
"It is someone who must know the Danish football system, the Danish league, the Danish agents and know the contractual conditions in relation to DBU regulations."
SønderjyskE sit 11th in the 12-team Superliga this season.