Halve the melon and remove the stones. Cut into quarters or eighths, peel and cut into large pieces.
Put the melon pieces in a large, clean glass with a lid, add the rock sugar, the cloves and the lime zest. Pour on the grappa and let it rest for 4 - 6 weeks. Shake the glass over and over again.
When the sugar has dissolved, filter off the liqueur and let it rest for at least 6 more weeks so that the flavors spread out. Then filter through a cheesecloth again if necessary. Depending on the melon, the liqueur turns out to be relatively sweet. If it is not sweet enough with the specified sugar content, you can add a little sugar solution after filtering.