Line a baking sheet with parchment paper and sprinkle 1/4 cup sugar all over the parchment.
Place watermelon rind in a saucepan and cover with water; bring to a boil, reduce heat to medium, and simmer until slightly softened, about 5 minutes. Drain, rinse, rinse saucepan, and return watermelon to saucepan.
Stir salt and enough water to cover into watermelon rind in the saucepan. Bring to a boil, reduce heat to medium, and simmer until softened, about 10 minutes. Drain, rinse, rinse saucepan, and transfer watermelon to a bowl.
Combine 1/2 cup water, 1/2 cup white sugar, and lemongrass in the same saucepan; bring to a boil, add watermelon rind, and stir to coat. Reduce heat to medium-low and simmer, stirring occasionally, until most of the liquid evaporates, about 30 minutes. Continue simmering, stirring constantly, until remaining liquid evaporates and watermelon rind has a gumdrop-like consistency, about 30 minutes more.
Transfer watermelon rind to prepared baking sheet and roll to coat with sugar. Store in an airtight container.