Place egg in a saucepan; cover with cold water. Bring just to a boil; cover and remove from heat. Let stand 12 minutes, then run under cold water to stop cooking. Peel egg and quarter.
In the same saucepan, bring 2 inches salted water to a boil. Add green beans and cook until crisp-tender, 3 to 5 minutes. Immediately run under cold water to stop cooking.
In a small bowl, whisk together lemon juice, oil, and mustard; season with salt and pepper. Store this dressing in a small airtight container.
Just before serving, dice avocado and add it to your premade salad, along with egg. Toss with dressing.