Bring a small saucepan of water to a rolling boil.
Carefully lower eggs into water and cook for 7 minutes for a medium-soft yolk.
Immediately transfer eggs to an ice water bath for 3 minutes to halt cooking, then peel and halve.
Whisk olive oil, lemon juice, salt, and pepper in a large mixing bowl to emulsify.
Incorporate baby arugula into the dressing and toss until evenly coated.
Divide greens across two plates and arrange avocado, tomatoes, and bacon on top.
Position halved eggs atop the salad and serve immediately.