Heat olive oil in a skillet over medium heat. Cook and stir onion and carrot in the hot oil until softened, about 4 minutes. Add garlic, thyme sprigs, kosher salt, black pepper, and red pepper flakes; cook and stir to coat, 1 minute.
Stir lentils, tomatoes and their juice, and chicken stock into onion mixture. Cover and simmer until lentils are tender, about 40 minutes. Add kale, lemon zest, and lemon juice; cook until kale is wilted, about 5 minutes. Season with salt and black pepper.
