Peel, quarter and chop the tomatoes; place in a colander to drain. Transfer to a Dutch oven; add apples and lemons. Cook and stir over medium heat for 15 minutes. Add sugar and ginger. Tie cloves in a cheesecloth bag; add to the pot. Bring to a boil, stirring occasionally, and cook until sugar has dissolved. Reduce heat; simmer for 40 minutes, stirring frequently.
Remove spice bag. Carefully ladle hot mixture into nine hot half-pint jars, leaving 1/4-in. headspace. Remove air bubbles and adjust headspace, if necessary, by adding hot mixture. Wipe rims. Center lids on jars; screw on bands until fingertip tight.
Place jars into canner with simmering water, ensuring that they are completely covered with water. Bring to a boil; process for 10 minutes. Remove jars and cool.
The processing time listed is for altitudes of 1,000 feet or less. Add 1 minute to the processing time for each 1,000 feet of additional altitude.