Fill a large saucepan with heavily-salted water and bring to a boil. Add 1 cup barley and 1 cup lentils, stir occasionally to dislodge any lentils that get stuck to the bottom, and cook until al dente, about 20 minutes. Lower the heat a little bit if it looks like the pot is going to boil over. During the last 2 minutes of cooking, add the 8 ounces chopped green beans and boil until knife tender.
Meanwhile, combine the 2 cloves minced garlic, 3 tablespoons lemon juice, 2 tablespoons apple cider vinegar, 2 teaspoons dijon mustard, 1 teaspoon salt, 1 teaspoon thyme, and 1/4 teaspoon black pepper in a large bowl that you will serve the salad in. While constantly whisking, slowly add the 1/3 cup olive oil until incorporated. Making the dressing right in the salad bowl will mean 1 less bowl for cleaning—yay!
Once barley and beans are tender, drain thoroughly through a colander and add to dressing while still warm so they soak up as much dressing as possible. Toss to combine, then add the 1 1/2 cup cherry tomatoes, 1/4 red onion, 3/4 cup feta cheese, and 2 tablespoons chopped oregano. Stir gently and taste; adding more salt and pepper if necessary. Serve warm, room temperature, or cold.