1. Cut rind off watermelon and discard. Cut fruit into 1/2-inch chunks.
2. Line a 10- by 15-inch pan with plastic wrap. Arrange fruit on wrap in a single layer. Freeze until firm, 1 to 2 hours; if making ahead, transfer frozen chunks to a freezer bag.
3. In a blender, combine half the pineapple juice, rum, and lemon juice. Whirl, gradually dropping in half the frozen watermelon chunks, until smoothly puréed. Sweeten to taste with sugar and pour into a pitcher or directly into glasses. Repeat to make a second batch.