Put the lentils and barley in a saucepan with cold water to cover by about 2 inches. Season with salt, and bring to a boil over high heat; reduce the heat and simmer, uncovered, until the lentils and barley tender, about 20 minutes. Drain excess liquid and put the beans and grain into a large bowl. Cool.
Meanwhile, melt the butter in skillet over medium heat and cook the onion, garlic, and ginger until the onion is tender, about 4 minutes. Stir in the curry powder and cook until aromatic, about 1 minute more. Cool slightly and then add to the lentils and barley.
Stir the cilantro, bread crumbs, and eggs into the lentil mixture, and season with 1 teaspoon salt and pepper, to taste. Puree 1 cup of the burger mix in a food processor until smooth. Return puree back to the bowl and mix well. Form mixture into 6 burgers (about 1/2 cup each). Place on a plate and refrigerate for 1 hour.
Preheat oven to 400 degrees F.
Heat 1 tablespoon of the olive oil in a nonstick skillet over medium-high heat. Season burgers with salt and pepper and cook 3 burgers, turning once, until golden brown on both sides, about 5 minutes in all. Transfer the browned burgers to a baking sheet. Repeat with the remaining oil and burgers. Transfer burgers to the oven, and cook until firm, about 10 minutes.
Meanwhile lightly toast buns or pitas. Mix the goat cheese and yogurt in a small bowl until smooth, season with salt and pepper. Put the burgers on the buns, and top with cheese and lettuce, cucumber, radish, and/or a squeeze of lime juice, if desired. Serve.
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