In a blender or food processor, combine the ginger with 1 cup of water and blend until smooth.

Strain the blended ginger through a fine mesh sieve into a large bowl, pressing down to extract as much juice as possible.

In a saucepan, combine the sugar with 1 cup of water and heat over low heat, stirring until the sugar dissolves to make a simple syrup.

Allow the syrup to cool, then mix it with the ginger juice in the bowl.

Add the remaining 2 cups of water, lemon juice, and yeast to the ginger mixture, stirring well.

Transfer the mixture to a clean, plastic or glass bottle with a tight-fitting cap, leaving about an inch of headspace.

Seal the bottle tightly and let it sit at room temperature for 24 to 48 hours to ferment.

Once it reaches your desired fizziness level, refrigerate the ginger beer and serve chilled.