Put the chicken thighs in a bowl. Cut the lemon in half and squeeze out the juice— do not discard the lemon!
Add the lemon juice, a tablespoon of olive oil, a chopped garlic clove, and some salt and pepper to the chicken. Mix everything well and leave to marinate for at least 2 hours. Longer is allowed, even preferred!
Preheat the oven to 200 degrees.
Wash the potatoes, dry them, and cut them in half if necessary. Peeling is not required. Wash and peel the carrots and cut them into chunks. Put the potatoes and carrots in a baking dish and add a generous tablespoon of olive oil. Add the other finely chopped garlic clove and the leaves from the thyme sprigs. Add salt and pepper and stir well.
Place the lemon chicken in the sheet pan as well. Slice the lemon and divide it over the chicken and the rest of the traybake. Bake the traybake with chicken for 40 minutes. Cover the dish with aluminum foil for 25 minutes, then remove it.
Remove the lemon pieces, spoon the contents of the lemon chicken traybake onto two plates, and serve immediately.