It was in 1939 so well before dna testing. Maybe they could have done it when dna testing became available but I don't think the family were interested so maybe they refused. Lina's son died in 1979, when he was 40, so it would have had to be collected posthumously from both Lina's son and father. Maybe that wasn't possible for some reason or another.
There's not a lot of information on the police investigation.