Peel the green outer layer from the watermelon rinds using a sharp knife, then chop the inner white portion into small, even pieces.
Place the chopped rinds into a large saucepan and add enough water to cover them. Bring to a boil over medium-high heat and cook for 10 minutes until the rinds are tender. Drain and rinse with cold water.
Add the drained rinds back to the saucepan. Pour in 2 cups of water and bring to a simmer. Cook, stirring occasionally, until the rind mixture softens further and starts to become translucent, about 15 minutes.
Stir in the sugar, lemon juice, and grated ginger. Increase heat to medium and bring the mixture to a gentle boil, stirring constantly.
Reduce heat to low and cook the jam, stirring frequently, until it thickens and reaches a glossy, sticky consistency, approximately 30 minutes. The jam should hold its shape on a spoon and show some hairline
Pour the hot jam into sterilized jars, leaving a small headspace. Seal with lids and allow to cool at room temperature before storing in the refrigerator or pantry.