Place Medjool dates in a bowl and cover with hot water. Let sit for 10 minutes. Once softened, take the dates out of the bowl, remove the skin and pits from dates, and mash with a fork.
Combine cranberries, date paste, lemon juice, zest, and water in a saucepan. Bring to a boil, then reduce heat and simmer for 10 minutes, until starting to thicken. Remove from heat and let cool completely.