1. Place 10 pop sticks in a bowl of warm water.
2. Grate ginger over a bowl, collecting the juice. Add honey and 1 cup warm water; stir until honey has dissolved. Stir in another 1 1/4 cups water. Place in refrigerator to allow ginger to steep. When mixture is cold, strain into a 4-cup measuring cup. Stir in lemon juice and pour mixture into molds.
3. Place lid on top and insert damp pop sticks. Place mold in freezer and freeze for 8 to 12 hours.