Mix 1/3 cup lemon juice, melted margarine, 1/2 teaspoon thyme, garlic powder, cumin, and red pepper flakes in a bowl. Pour and rub lemon juice mixture over Cornish hens. Mix 1/2 teaspoon thyme, salt, and black pepper in a bowl; sprinkle over Cornish hens.
Pour chicken broth and 1/3 cup lemon juice into a slow cooker.
Place about 1 tablespoon chilled margarine in the cavity of each hen; place hens in the slow cooker. Arrange the remaining margarine cubes in the chicken broth mixture.
Cook hens in the slow cooker on High for 4 hours or Low for 8 hours.