In a large, deep, straight-sided skillet or heavy pot, combine carrots, celery, onion, lemon, 1 1/2 teaspoons salt, and 6 cups water. Bring to a boil; reduce to a simmer, cover, and cook 8 minutes.
Season salmon with salt and gently lower into simmering liquid (liquid should just cover fish). Reduce to a very gentle simmer. Cover and cook until salmon is opaque throughout, about 5 minutes (longer for thicker fillets). Using a wide slotted spatula, remove salmon from liquid.