What theme (lesson about life) does Beowulf's defeating evil, in the form of Grendel and Grendel's mother, yet losing his own life, suggest about the struggle between good and evil?

To answer the question, I will start with a discussion of Beowulf’s death. During his battle with the dragon, the creature deals him a deadly blow when its tusks enter their poison into Beowulf's bloodstream; however, this is not an instantaneous death. Beowulf's final action is to split the dragon in two with his dagger. While Beowulf does die from his wound, he also still defeats the dragon.
This shows that good always triumphs over evil, but certain sacrifices have to be made.
The way this relates to the elements of this Old English epic are its inclusion of an epic hero. The epic hero is a man of noble character and extreme courage, like the idea of a perfect person. The epic hero is willing to do whatever it takes to defeat the evils that threaten his people, to whom he is undoubtedly loyal. All that Beowulf accomplishes is in service of others: each monster he defeats was hurting people. To stop the evil from continuing to ravage the land, Beowulf willingly sacrifices his life. Therefore, his death is not proof that evil wins, but rather further evidence that good will go to great lengths in vanquishing evil.