This refreshing drink tastes like summer in a glass!
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Cut 1 lemon in half lengthwise through both ends. Lay lemon halves, flat side down, on cutting board, then cut each half crosswise into thin semicircles; discard ends. Put half of lemon slices in large pitcher and set aside. Put remaining lemon slices in large bowl and add watermelon and sugar.
Use potato masher to mash sugar, lemon slices, and watermelon together until sugar is completely wet, about 1 minute. Set aside.
Cut remaining 6 lemons in half crosswise. Use citrus juicer to squeeze juice into liquid measuring cup. You should have a little over 1 cup. (Save any extra juice for another use.)
Pour lemon juice and water into bowl with lemon slices, watermelon, and sugar. Use rubber spatula to stir mixture until sugar is completely dissolved, about 1 minute.
Set fine-mesh strainer over pitcher. Carefully pour mixture through strainer. Use rubber spatula to press on lemons and watermelon to get out as much juice as possible. Discard lemon slices and watermelon in strainer.
Mashing sliced lemon with granulated sugar extracts oils contained in the peel and punches up the lemon flavor. Try to purchase large lemons that give to gentle pressure; hard lemons have thicker skin and yield less juice.