Working in two batches, cook beans in a large pot of boiling, generously salted water just until crisp-tender, about 5 minutes. Using tongs, transfer to a colander set in a bowl of ice water; let cool. Drain well, then pat dry with paper towels.
Toss beans, oil, 2 tablespoons mint, 1 tablespoon dill, 1 tablespoon lemon zest, 2 tablespoons lemon juice, and half of feta in a large bowl; season with salt, pepper, and more lemon juice, if desired. Serve beans topped with remaining feta, 2 tablespoons mint, 1 tablespoon dill, and 1 tablespoon lemon zest.
DO AHEAD: Beans can be cooked 1 day ahead. Wrap in a paper towel, place in a resealable plastic bag, and chill.
