Discard any soft or decayed cranberries. Cut lemons into 1-in. chunks and discard seeds.
In a food processor, pulse lemon chunks until coarsely chopped. Add cranberries and pulse until berries are barely chopped.
In a medium saucepan, mix fruit and 1 cup sugar. Bring to a boil over high heat. Reduce heat and simmer, stirring often, until flavors are blended, about 5 minutes.
Make ahead: Cover and chill up to 1 week.
Note: Nutritional analysis is per 3-tbsp. serving.