Place cabbage in a large kettle; add diced apple, 2 teaspoons salt, lemon juice, and water. Bring to a boil. Reduce heat, cover, and simmer, stirring occasionally, for about 15 minutes.

Warm butter in a skillet over medium-high heat. Sauté onion until golden. Add onion to cabbage mixture along with 1 teaspoon salt, pepper, vinegar, and sausage. Cook, covered, until sausage is heated through, 20 to 30 minutes.

Spoon cabbage onto a heated platter and top with sausage to serve.