When Sicilians cook seafood, they rarely add herbs or seasonings, but in this unusual salad the fragrant celeriac and celery add herbal depth, as well as a welcome crunch.
Combine water, bay leaves, onion, garlic, salt, ¼ cup lemon juice, and ¼ cup olive oil in 2-3-quart nonaluminum saucepan. Cover and boil gently 15-20 minutes.
Meanwhile, cut squid across into ⅛-¼-inch rings. Cut tentacles into bite-sized pieces, if large; place in mixing bowl.
Strain solids from stock; return liquid to saucepan. Add squid and simmer 1