Cook raspberries. Add the raspberries and water to an 8-quart pot. Place over medium heat and simmer. Once simmering, lower the heat to low and cook for 20 minutes.
Strain. Transfer the raspberries to a fine mesh strainer or jelly bag placed over a bowl. If you do not have one, line a strainer with 3 layers of cheesecloth. Allow the raspberries to drain for 2 hours.
Prep for canning. Prepare your jars for canning by washing them in hot, soapy water. Transfer jars to a water bath canner and fill the canner so the jars are fully submerged in water. Place the canner over medium heat and simmer. Add the canning lids and rings to a saucepan with water. Place them over medium-low heat and simmer.
Press solids through strainer. Using a spatula, press the remaining liquid out of the raspberry mixture. You want a total of 4 ½ cups of liquid. Discard the seeds and pulp.
Add sweeteners and lemon. Transfer the raspberry juice to a clean 8-quart pot over medium-high heat. Add the corn syrup, sugar, and lemon juice. Stir the mixture so the sugar dissolves completely.
Boil. Bring the mixture to a full rolling boil, stirring constantly. Once it hits a full rolling boil, boil for 2 minutes. After 2 minutes, remove from the heat.
Skim foam. Skim foam off the top of the syrup (optional but recommended).
Fill jars. Add the hot syrup to the hot jars by placing a canning funnel over the hot jar, ladling in the syrup, leaving a ¼ inch headspace. Repeat this process until all of the syrup is added to the jars.
Clean rims and fasten lids and rings. Wipe the rims of the jars with a clean, moist towel. You may want to use a white vinegar-moistened towel to make sure there is no syrup left on the rims. Place the lids and rings on the jars. Tighten the rings so they are fingertip-tight.
Process. Place the filled and lidded jars back into the water bath canner. Make sure the jars are fully submerged with at least 1 inch of water above them. Place the lid on the canner, set the heat to medium-high heat, and allow the canner to come to a boil. Once the water is boiling, set a timer for 10 minutes and process the jars.
Rest. After 10 minutes, remove the canner from the heat. Remove the lid and allow the jars to sit for 5 minutes.
Cool and check seals. Transfer the jars to a heat-proof area so they can cool for 12-24 hours. The next day (after 24 hours), check the jars for a proper seal.
Store. Once a proper seal has been confirmed, remove the rings and store the jars in a cool, dark place for up to 18 months or per your lids manufacturer’s recommendations.