Step 1 Fill a stainless steel or other nonreactive pot or container (do not use aluminum) with 12 cups of water. Stir the pickling lime into the water. Set aside for 1 to 2 hours, then pour the clear water into another nonreactive pot or container (discard the lime at the bottom). Set aside for another hour to give the remaining lime time to settle, then pour off the clear liquid into another nonreactive container, discarding the lime at the bottom.
Step 2 Cut the watermelon rind into finger-sized chunks or pieces and toss them into the strained water. Set aside to soak for 3 to 4 hours, then drain and rinse thoroughly several times.
Step 3Meanwhile, in a medium, heavy-bottom pot, combine the sugar with the remaining 2 cups of water. Heat over medium-high heat until the sugar dissolves and the mixture comes to a boil. When the mixture begins to thicken, add the lemon juice and bring to a boil again. Carefully add the watermelon chunks. Simmer over medium heat until the pieces take on an amber shade and are mostly transparent, about 45 minutes. Remove from heat. Strain the watermelon pieces using a slotted spoon and set aside to cool on a sheet of parchment paper.