Sort and wash lima beans; place in a small saucepan. Cover with water to 2 inches above beans, and bring to a boil. Cover, reduce heat, and simmer 20 minutes or until tender. Drain.
Cook wax and green beans in boiling water 5 minutes or until tender. Drain and plunge beans into ice water; drain.
Combine lima, wax, and green beans in a large bowl. Add vinegar, olive oil, salt, and pepper; toss well. Top with cheese and slivered almonds.