Juice four large cucumbers in a vegetable juicer. Strain the juice.
Combine the cucumber juice, sugar, calcium lactate and salt in a large bowl. Blend with an immersion blender until powder ingredients are completely dissolved.
Using a syringe, draw cucumber juice mixture from the bowl and expel into hemispheric mold until all hemispheres are filled. Place the mold in the freezer until the molds are completely frozen. Reserve remaining cucumber juice in a mason jar and refrigerate.
In a separate bowl, combine 1000 g of filtered water with the sodium alginate, adding sodium alginate gradually and blending with immersion blender until all clumps are gone. Strain sodium alginate mixture into a new bowl.
Warm sodium alginate bath in microwave or on stove and allow to settle so no bubbles are present.
Drop frozen cucumber juice hemispheres into sodium alginate bath, taking care to prevent them from coming into contact with one another. Allow them to melt in the bowl.
Spoon spheres out one at a time with spherification spoon. Rinse each sphere twice by dipping once into two separate small bowls of water. Drop rinsed sphere into jar of reserved cucumber juice. Repeat until all spheres are created.