In a large, heavy pot, heat oil over medium-low heat. Add onions and cook, stirring frequently, for 5–7 minutes or until soft and translucent. Add garlic and cook, stirring for 2 minutes. Add tomatoes and vinegar, increase heat, and bring to a boil. Reduce heat and simmer, uncovered, stirring occasionally for 60–70 minutes or until thick and reduced by about half.

Meanwhile, heat three 2-cup jars and lids.

Working in batches, purée tomato mixture in a food processor. Return to pot and bring to a boil. Reduce heat and simmer, stirring occasionally, for 30 minutes or until thick. Add basil, oregano, lemon juice, and salt.

Fill hot jars, leaving 1/2-inch headspace. Top with lids. Process jars at a full boil for 30 minutes.