The 38-year-old forward star led Luleå to the club's first Swedish Championship gold in 29 years last season and then left Norrbotten.
In September, Omark signed a short-term contract with Lugano through October and scored 11 points, 4 goals and 7 assists, in 15 games before last week's international break.
Now the club claims that Omark chose not to extend his contract for family reasons.
"The Omark family does not believe that the proposed school alternatives in Switzerland are suitable for their daughters," Lugano writes on its website.
