Add the cranberries and water to a large saucepan. Place over medium-high heat and bring the mixture to a gentle boil.
Cook for 15 to 20 minutes, stirring occasionally. The cranberries will soften, burst open, and release their juices into the water.
Remove the saucepan from the heat. Using a potato masher or large spoon, gently mash the softened cranberries to release additional juice and flavor.
Allow the mixture to rest for about 5 minutes.
Place a fine mesh strainer over a large bowl or pitcher. Carefully pour the cranberry mixture through the strainer.
Let the liquid drain naturally. Press gently on the solids with the back of a spoon to extract as much juice as possible.
While the juice is still warm, stir in the granulated sugar until fully dissolved.
Add the lemon juice and stir well to combine.
Taste the juice and adjust sweetness if desired.
Allow the juice to cool completely at room temperature.
Transfer the juice to a covered container and refrigerate for at least 2 hours or until thoroughly chilled.
Stir before serving and pour over ice if desired.