Working in batches, puree watermelon in a blender. Strain through a fine-mesh sieve into a large bowl (discard solids). Puree strawberries; add to bowl. Add sugar and lime juice and stir until sugar has completely dissolved.
Pour mixture into ten 3-ounce ice-pop molds and insert sticks. Freeze pops until solid, 2 1/2 to 3 hours (or up to 1 week).