I really can’t foresee LH rejecting any of the tests I’ve paid for in Denmark and in Sweden when flying SAS and/or Lufty on the way back to the US this year. If the Danish or Swedish test center says it issues test results in English that are good for travel and delivers just that, then SAS and Lufthansa seem to routinely accept them easily as long as they seem timely.

LH is no more challenging than SK in this regard. There are two gate-keepers potentially: the airline reps doing check-in (and potentially boarding) at CPH; and the airline reps doing document checks in Germany.