Writer Ron Rosenbaum, who has been corresponding with Dmitri Nabokov about this issue for the last two years, reveals a fascinating dilemma in Slate:

It’s the question of whether the last unpublished work of Vladimir Nabokov, which is now reposing unread in a Swiss bank vault, should be destroyed – as Nabokov explicitly requested before he died.
… It’s a decision that has fallen to his sole surviving heir (and translator), Dmitri Nabokov, now 73. Dmitri has been torn for years between his father’s unequivocal request and the demands of the literary world to view the final fragment of his father’s genius, a manuscript known as The Original of Laura.
Dmitri’s predicament goes beyond Laura. It’s one that raises the difficult issue of who “owns” a work of art, particularly an unfinished work of art by a dead author who did not want anything but his finished work to become public. Who controls its fate? The dead hand from the grave? Or the eager, perhaps overeager, readers, scholars, and biographers who want to get their hands on it no matter what state it’s in?
… Dmitri’s past pronouncements suggest that Laura is not merely another scrap of paper. At one point he called it “the most concentrated distillation of [my father’s] creativity.”