Your question can't be answered within few sentences. And it can't be answered by single persons alone. But I dare to write my share here, because I was and still am into several flavours of Metal including DM. And it was a significant part of my cultural development.
First I want to share some general opinions for which I do not have any proof whatsoever. Then I'll try to explain my personal perception.
I guess we have to go back into history. Metal is an offspring of Hard Rock or rock music in general. Emerging music styles frequently are a way for their fans to differentiate or even isolate themselves from the mainstream. And music mainstream often is a pars pro toto for a whole society.
IMO as the influence between musicians and their fans is bidirectional and often immediate, the bands bring up the style and content that allow the fans to use the music for their identification.
While Hard Rock turned against the philistinism and social conventions Metal had to part company at least partially, to make its own point.
Now I'll change to my personal view. Born in the middle of 70ies I grew up during the apex of cold war. I grew up in a country which many strategists predicted to be the first tactical nuclear battlefield when the cold war once turned hot.
Surrounded by a heavily industrialized economy environmental pollution was omnipresent and the doomsday clock was on three before 12.
My whole youth was infused by dystopies. While I clearly percieved the menace, I could watch the ones in power just go on as they ever did, apparently ignoring all threats and dangers they piled up on the surface of the planet.
There was no positive imagination of the future one could easily grasp in the 80ies. So my mood as a teenager was clearly dystopic.
As it comes with teenage it is not easy to utter such perceptions and to live with while considering the very own existence somehow futile and powerless.
One method of coping with dystopic and isolating feelings is to suck up similar views. This can be music, books or movies.
For me it were the various flavours of Metal which provided a high percentage of social crticism and dystopic depiction wrapped in rough language and sound able to support that mood I was forced into. I guess many of my friends felt similarily.
If you look closer to the lyrics, you can observe that many deal with great problems of mankind and apply heavy criticism on it. I did not expect the music to change the world, but I felt good listening to it when it confirmed my view on the world in political and social perspectives.
This made the music more earnest to me than the average popmusic lovesong and eventually more valuable.
So my resumee is: Apparently evil lyrics in Metal and especially Death Metal are based on the sociocritic attitude of the genre. This was fostered by the bad future in the 80ies.