Watermelon rind preserves have little natural pectin (only the lemon slices) and will basically be candied watermelon peel suspended in a thickened syrup. It won't "set" like a jam. The only way to achieve something thicker would basically be to keep cooking to evaporate the water out, but it's not a "set" per se, and will have a more caramelized taste.

If you would like more ginger flavor, you could cook some thin slices of fresh ginger with the rind and then remove it before bottling up, or you could add a little crystallized ginger to the jars. Other options would be a bit of ginger juice, ginger syrup or dried ginger pieces. But be careful. Flavors can alter during processing and after sitting on the shelf for a while, so it's easy to overdo it.

You can leave the lemon in, distributing between jars for some color and contrast, or you can take it out, it's up to you.

Carol

thanks Carol
it would have been nice if the recipe said so.
the lemon peels left over taste like candied ones.. but better than store bought
thanks
Jean

What I am able to remember from eating Watermelon preserves was the clove flavor. It seems like they used pickling spices. We did not have much so I do not expect there was any ginger unless it was the powder. I also do not remember it being set as we ate the watermelon chunks. But that was over 53 years ago. Just the thoughts and the taste that come back to mind