Peel and finely chop ginger. In heavy saucepan, mix ginger with sugar and water. Bring to a boil over medium heat. Continue cooking an additional 30 minutes.
Remove saucepan from heat and stir in lemon zest. Let syrup cool to room temperature, then strain through fine mesh sieve. Store syrup, covered, in refrigerator up to 2 weeks.
Ginger Meyer lemon soda:
Partially fill tall glass with ice cubes. Pour 2 tablespoons ginger syrup over ice, then add club soda. Serve as is, garnished with thin slice of Meyer lemon, or stir syrup and club soda together before garnishing with lemon and serving.