If Beren had not died

From the Silm:

But the wise have said that the Silmaril hastened their end; for the flame of the beauty of Lúthien as she wore it was too bright for mortal lands.

Had Lúthien not become mortal, they would have both probably lived longer (and perhaps they would have stayed in Doriath as well).

The only reason I bring this up is that after the Quest ended, the Fëanorions were unwilling to assault Beren and Lúthien. Remember, it was only after the death of Lúthien that Doriath was attacked.

Of course, after Beren's death, Lúthien might have died of grief anyway and everything come to pass in the same manner, but there's a distinct possibility that a lot would have been different.