In a medium saucepan with a tight-fitting lid, combine the prunes and water and let them sit for 2 hours to soften. (If the prunes are cut in half, it will take only 1 hour.) Bring the water to a boil, cover the pan tightly, and simmer for 20 to 30 minutes on the lowest possible heat until the prunes are very soft when pierced with a skewer. If the water evaporates, add a little extra.

In a food processor, place the prunes and any remaining liquid, the sugar, and lemon zest and process until smooth.

Scrape the prune mixture back into the saucepan and simmer, stirring constantly with a wooden spatula or spoon to prevent scorching, for 10 to 15 minutes, or until it is a deep rich brown and very thick. A tablespoon of the mixture when lifted should take about 3 seconds to fall from the spoon. Transfer the lekvar to a small bowl and let it cool completely.