Using a vegetable peeler or paring knife, gently peel off the rind of both lemons, being sure to not include any of the white pithy parts. Add the lemon peels, water, sugar, and the cinnamon stick to a small pot over medium heat. Bring to a boil, then reduce the heat and simmer until the lemon peels are tender and slightly translucent, about 6 to 8 minutes. Strain the lemon peels, discard the cinnamon stick and reserve the liquid in a measuring cup.
In a food processor add the cherries, lemon peels, and a tiny pinch of salt, to taste. Pulse while slowly adding the reserved liquid, about 1/4 to 1/2 cup, until the consistency of cranberry sauce or relish is achieved. Use the remaining reserved liquid to flavor iced tea, if desired. Taste and add fresh lemon juice to balance the sweetness. Spoon the relish into a bowl, cover and refrigerate until ready to serve.