Prepare the raspberry syrup: In a saucepan, combine the raspberries, water, lemon juice, sugar, and maple syrup and bring everything to a soft boil. Using a fork, separate and crush the raspberries. Let the mixture reduce for 10–15 minutes on medium-low heat. Pour the mixture into a fresh bowl through a mesh strainer to remove seeds. Add a little bit of the strained syrup (about 1 tbsp) back to the discarded seeds to get all the flavor, then discard the rest of the seeds. Let the resulting raspberry syrup cool to room temperature.