Place the turkey carcass in the pot or Dutch oven, and cover with the water. Place over medium-high heat, and when the water reaches a gentle boil, reduce the heat to low. Use a large fine-mesh sieve or ladle to skim any scummy stuff that's formed on the surface, then lid the pot and simmer for 1 hour.
Position a colander over another pot, or large heavy mixing bowl or other container, and carefully strain the broth (watch out for steam). If you're going to continue cooking in the original pot, rinse it out thoroughly then pour the strained liquid back into it.
Return the pot to medium heat, and season the broth with 1 tablespoon of salt, the black pepper, Old Bay, and thyme. Add the turkey meat and the carrots and cook for 5 minutes, adjusting the heat to maintain a simmer. Add the orzo and continue cooking for 10 minutes stirring occasionally. Add the green beans and cook 5 minutes, adding the peas when one-minute remains.
Finish with the lemon juice and season with additional salt if desired.