First, prepare the dressing. In a medium bowl, combine the olive oil, fresh lemon juice, and dill with a whisk. Add salt and pepper, to taste. Set aside.
Fill a saucepan with a few inches of water and bring to a simmer over high heat. Once at a gentle simmer, lower the heat to keep the water from reaching a rolling boil.
Crack one egg into a small glass bowl, then gently lower the egg into the water. Repeat with the second egg, keeping some distance between them. Cook the eggs for about 4 minutes, until the whites are just set. Remove the eggs with a slotted spoon and place on a folded paper towel to drain.
Split the salad greens between two serving bowls and top each salad with half of the smoked salmon slices. Add one poached egg to each salad and season with salt and pepper, if desired. Drizzle a little lemon-dill dressing over the salads and serve immediately.