The trembling starlight of the skies
He saw there mirrored shimmering.
Tinúviel the elven-fair,
Immortal maiden elven-wise,
About him cast her shadowy hair
And arms like silver glimmering.
Long was the way that fate them bore,
O'er stony mountains cold and grey,
Through halls of iron and darkling door,
And woods of nightshade morrowless.
The Sundering Seas between them lay,
And yet at last they met once more,
And long ago they passed away
In the forest singing sorrowless.
Beren and Lúthien resided on the isle of Tol Galen, the fairest land east of Valinor (land of the gods, elves, and immortals). The beauty of Lúthien, wearing the incredibly beautiful necklace imbued with a silmaril, residing in such a pretty land was too bright for mortal lands to bear, and hastened their demise. 
 Finally, having sired a son and grandson, Beren and Lúthien died. 
 Elves (and evidently Aragorn) continually mourn the loss of Lúthien, the only elf to have been lost (until Arwen’s death), and the fairest being to have ever lived. 
 This sense of loss was surely echoed in Tolkien’s own life, when Edith died in 1971, and J.R.R. survived her for the remaining 21 months of his own.