Pour the cold tomato juice into a saucepan or pot large enough to comfortably hold all of the juice. Heat over medium heat until the juice is hot but not quite boiling. Stir frequently with a wooden spoon to ensure the juice heats evenly.
Put 2 tablespoons of lemon juice in each empty quart jar and 1 tablespoon in each empty pint jar.
Ladle the tomato juice into canning jars. Fill each jar almost full, leaving about 1/2 inch of space at the top of each jar. Place a lid on each jar and screw the lid on with a ring, just finger tight.
Process the jars in your preferred style of canner. If you are using a water bath canner, process pints for 35 minutes and quarts for 40 minutes if your altitude is under 1,000 feet. If your altitude is over 1,000 feet, add five minutes per 3,000 feet.
Remove the canned jars of tomato juice from the canner with tongs. Allow them to cool overnight on a flat surface in a draft-free area. Press on the lid of each jar when they cool to ensure they all sealed properly. If the lid pops inward when you push on it or sticks up, rather than lying flat or curving slightly downward, that jar did not seal properly.