Kristina, I'm afraid I have no further information on Nikolai Gudim Levkovic. I have seen his big grave in Geneva and I myself wondered who he was. A book about the cemetery in which he is buried has only this to say:
"Etablie tout au bord du chemin transversal, une très ancienne concession (no 251) a été offerte à un jeune étranger. Le prénom NIKOLAI est écrit en gros caractères cyrilliques. Sur un côté du monument, quelques lettres sont encore discernables, et l'inscription intéressera peut-être les amateurs d'onomastique. Nous lisons: Nikolai Viktorovitch Gudim Levkovitch (1846-1867)."
There is no other information about this grave and the lettering in cyrillic is very faded. When did your great-grandmother live in Geneva? Surely later than the date of Nikolai's death in 1867? I'm afraid I don't understand Italian so if you could reply in English or French it would be easier for me.
Best, Fiona