The normal terms and conditions for Lønsikring says that you only can get the insurance payment from Lønsikring if you at the same time are qualified for "normal" Unemployment benefits from your A-kasse.
However it was how it worked before the new residence requirement that came in to force from january 1, 2019.
At the moment we are not aware of how the new residence requirement will affect Lønsikring. But until we have time to investigate all the individuel Lønsikring offered by the A-kasser in Denmark, we must keep to the conditions that previous applied: You can only get paid from Lønsikring, if you are eligible for Unemployment benefits ("dagpenge").
This means that if you are not eligible for dagpenge, because you dont meet the new residence requirement, then you will probably also not qualify for payments from lønsikring.
BUT we strongly recommend you to get this confirmed by the A-kasse/company where you bought the Lønsikring.