Add the cranberries, sugar, and water to a medium saucepan. Stir to combine and place over medium heat.
Cook for 3 to 4 minutes, stirring occasionally, until the sugar has completely dissolved into the liquid.
Continue simmering for 8 to 10 minutes. As the cranberries heat, they will begin to burst and release their juices.
Stir in the lemon juice and lemon zest and mix well to combine.
Use a potato masher or the back of a spoon to mash the softened cranberries to your desired consistency.
Continue cooking for 3 to 5 minutes, stirring occasionally, until the jam thickens and becomes glossy.
Test the consistency using the chilled plate method. If needed, cook for an additional 1 to 2 minutes.
Remove the saucepan from the heat and allow the jam to cool for 15 to 20 minutes.
Transfer the jam to a clean glass jar or airtight container.
Refrigerate until completely chilled and ready to serve.