Cook lentils.
Place lentils and 1 teaspoon salt in a medium saucepan; bring to a simmer and cook until just tender, 25 to 30 minutes. Drain well and transfer to a large bowl. Occasionally toss with a spoon to let steam escape.

Prepare eggs.
Meanwhile, bring a small saucepan of water to a boil. Gently lower in eggs. Reduce heat to medium; simmer for 11 minutes. Transfer to a bowl of cold water.

Make dressing.
While eggs cook, whisk vinegar, mustard, and remaining 1/2 teaspoon salt in a medium bowl. Add oil in a steady stream, whisking constantly, until dressing is well combined.

Assemble the salad.
Add celery and olives to lentils in bowl. Add dressing; toss to coat. Peel and halve eggs.

Plate and serve.
Divide arugula among 4 plates. Top each with lentil mixture, 2 egg halves, 1 avocado half, 2 tablespoons pepitas, and pepper. Drizzle with oil and serve with lemon wedges.

Make-Ahead and Storage Instructions

Store, covered, at room temperature for up to 3 days. To freeze, wrap tightly, place in a freezer bag, and freeze for up to 1 month. Thaw at room temperature for 1 hour.