Heat the oil over medium-high heat in a large (at least 8-quart), heavy-duty pot or Dutch oven. Add the onion, leek, carrot, and 1/2 Tbs. salt. Cook, stirring occasionally, until the vegetables are softened and lightly browned in places, 4 to 6 minutes. Add the thyme and cook, stirring, until fragrant, 30 seconds.
Add the broth and bring to a boil. Reduce to a simmer and cook, stirring, until the vegetables are completely tender, 20 to 30 minutes.
Stir in the shredded chicken, egg noodles, and peas. Simmer, stirring occasionally, until all are tender and the flavors meld, about 10 minutes.
Stir in the parsley and 1 Tbs. of the lemon juice. Taste, and add more lemon juice, a little at a time, if needed, up to 4 Tbs. Season to taste with salt and pepper.