I assume that in this question you are referring to the fact that The Epic of Gilgamesh is said to have been recorded on tablets of Lapis Lazuli. If that is the case, the aim of this question is to seek modern stories that could be equated with The Epic of Gilgamesh, which would largely be a matter of opinion.
If the comparison necessitates that the work be an epic poem, there are several phenomenal pieces to consider written as recently as the 20th century, one of the most prominent being written by Louis Zukofsky. The epic poem "A" is a sprawling, ponderous work that weaves the historical and personal with an extensive reference to music throughout.
If the work does not have to be an epic poem, I believe that James Joyce's Ulysses would be an ideal choice. Bringing together the epic and poetic with masterful strokes, it is a work upon which tablets of Lapis Lazuli would certainly not be wasted.