Chop the celery into 1 inch pieces and add to the blender along with the lemon juice and water. Blend for a minute, until the celery is completely broken down and you are left with a slurry.
Put a mason jar or glass in the middle of a large bowl (to minimize a mess). Pour the celery slurry through a nut milk bag or cheesecloth, and use your hands to squeeze all the juice out. You can discard the fiber/pulp left behind.