Prepare ginger bug: To a 16-oz glass jar, add 1 cup filtered water and 1 tbsp each ginger and cane juice and stir to combine. Cover jar with paper towel or a coffee filter and secure with a rubber band. Let ferment in a warm place away from direct sunlight for 24 hours. Stir in 1 tsp each ginger and cane juice and let ferment in a warm place away from direct sunlight for another 24 hours. Stir well; mixture should fizz when stirred. If fizzy, proceed to Step 2. If ginger bug does not fizz, add 1 tsp each ginger and cane juice daily until it fizzes when stirred.

Prepare beer: In a saucepan, bring 3 cups filtered water to a boil. Add 2 tbsp ginger and remove from heat. Stir in ¼ cup cane juice and honey until dissolved. Cover and let steep for 30 minutes. Let mixture cool to room temperature. Stir in lemon juice.

Meanwhile, in a blender or food processor, purée strawberries. Arrange a fine-mesh sieve over top of a large pitcher or bowl. Strain strawberries through sieve into pitcher, pressing on solids; discard solids.

Using sieve, strain honey mixture and ginger bug into strawberry liquid. Stir to combine and pour into 1-qt glass bottle. Seal tightly with lid and let ferment in a warm place away from direct sunlight, opening bottle every 24 hours to release pressure, until mixture reaches desired taste and fizziness, 2 to 10 days. Refrigerate for up to 2 weeks.