Heat a saucepan of water over high heat and bring to a boil. Blanch green beans for 1-2 minutes to partially cook them. Drain and set aside until ready to use.
Heat 1 tsp olive oil in a large skillet over medium-high heat. Place each half of the 2 lemons on the heated skillet cut sides down until lightly charred, about 2 minutes. Remove from heat, set lemons aside.
Combine 1 tbsp olive oil, capers, and green beans in skillet. Squeeze lemons over mixture. Toss to coat and cook 1-2 minutes.
Remove from heat and sprinkle with feta, chives, and pepper.