Put eggs in a saucepan and cover with cold water by 1 inch. Bring to a boil, cover, remove from heat and stand for 11 minutes, then transfer to ice water for 5 minutes.
Peel eggs and coarsely grate them into a bowl. Fold in yogurt, Dijon, 2 teaspoons lemon juice, salt and pepper without mashing the egg completely smooth.
Toast only the cut faces of the sesame bagels under the broiler for 1 to 2 minutes and cool on a rack.
Halve and pit avocados, scoop out the flesh and cut into thick slices. Toss gently with the remaining teaspoon lemon juice.
Divide avocado slices among bagel bottoms and spoon the egg mixture over them in an even layer. Close with the tops and cut in half, then serve promptly or refrigerate until eating.