Place eggs in a small pot and cover with cold water. Bring to a boil, then simmer for 10 to 12 minutes until the yolks are fully set. Drain and cool in cold water for 5 minutes. Peel and cut into bite-size pieces.
Wash all vegetables under cold water and dry well. Chop the lettuce. Slice and chop the cucumber, onion, and tomato into small pieces.
In a small bowl, mix together the mayonnaise, lemon juice, black pepper, olive oil, honey, and salt until smooth.
In a large bowl, combine the chopped lettuce, cucumber, onion, tomato, and egg pieces.
Pour the dressing over the salad and toss gently to coat. Serve right away.