Place the ginger, sugar, and 125 ml of the water into a 3 L saucepan and set over medium-high heat. Stir until the sugar has dissolved. Remove from the heat, cover and allow to steep for 1 hour.
Pour the syrup through a fine mesh strainer set over a bowl, pressing down to extract all of the juice out. Chill quickly by placing over an ice bath and stirring or set in the refrigerator, uncovered, until at least room temperature is reached.
Using a funnel, pour the syrup into a clean 2 L plastic bottle and add the yeast, lemon juice and remaining filtered water. Place the cap on the bottle, shake gently to combine then leave the bottle at room temperature for 48 hours. Open and check for desired amount of carbonation. It is important that once you achieve your desired amount of carbonation that you refrigerate the ginger ale. Store in the refrigerator for up to 2 weeks, opening the bottle at least once a day to let out excess carbonation.