The first "DE" in your sentence refers to "they" (i.e. the people making sandwiches), whereas the second "DE" refers to "those" (i.e. sandwiches); not just "the" salmon sandwiches they make at this place in general, but a specific type of salmon sandwiches called "fristelse" - therefore "those").

The translation of your sentence would be:

"Lager DE fortsatt DE laksesmørbrødene som de kaller for 'fristelse'?"

"Do THEY still make THOSE salmon sandwiches called(/that they call) 'fristelse'"?

The meaning would not stay exactly the same if you were to start the sentence the way you suggested as an alternative. You suggested: "Lager de forstatt laksesmørbrødene ...."? This opening suggests a different continuation of the sentence. For example:

"Lager DE fortsatt laksesmørbrødENE her av/med røkelaks fra den lokale produsenten, eller bruker de røkelaks fra en annen leverandør nå?"

"Do THEY still make THE salmon sandwiches here using smoked salmon from the local producer, or do they use smoked salmon from a different supplier now?"