In a large skillet over medium heat, heat oil. Add onion and carrot and season with salt and pepper. Cook, stirring occasionally, until onions are tender and translucent, about 6 minutes. Add thyme and paprika and cook until fragrant, 1 minute.
Turn off heat and make vinaigrette: whisk together all vinaigrette ingredients and season to taste with salt and pepper.
Add lentils, herbs, nuts, and dressing to skillet with carrots and onions. Stir to combine, then let sit 10 minutes to allow lentils to absorb dressing. Transfer to serving bowl and serve immediately.