In a medium saucepan, combine the pumpkin puree and water. Stir well to dissolve the puree into the water.
Place the saucepan over medium heat and bring the mixture to a gentle simmer.
Add the brown sugar, ground cinnamon, ground ginger, ground nutmeg, and salt. Stir until the sugar is fully dissolved and the spices are evenly distributed.
Reduce the heat to low and let the mixture simmer for about 10 minutes, allowing the flavors to meld together. Stir occasionally to prevent sticking.
Remove the saucepan from heat and allow the pumpkin juice to cool for a few minutes.
Once cooled, stir in the lemon juice. For a smoother texture, you can strain the juice through a fine-mesh sieve if desired.
Transfer the pumpkin juice to a pitcher and refrigerate until chilled, about 1 hour.
Serve the pumpkin juice cold in glasses, topped with a dollop of whipped cream and a sprinkle of cinnamon if desired.
Notes
For a smoother texture, strain the juice through a fine-mesh sieve.