In some cases the obstruction is 2-torsion, such as in Koschorke's example, which is an immersed surface (formed from 3 Möbius bands, with a triple point) that does not lift to a knotted surface, but it has a double cover that does lift.
In some instances, obstruction is 2-torsion, such as in Koschorke's example, which is an immersed surface (formed from three Möbius bands with a triple point) that does not rise to a knotted surface but has a double cover that does lift.