Melt butter in a small saucepan over medium heat. Add onion and garlic and cook, stirring occasionally, until very soft; do not brown. Remove from heat and set aside to cool.

Cut chicken, turkey, or salmon into 1 inch cubes then finely shred or flake (this goes quickly on low speed in the bowl of a stand mixer fitted with the paddle attachment). Add lemon juice, stock, Worcestershire, and onion mixture and combine; taste and adjust seasoning with salt, pepper, and cayenne as desired. Fold in eggs and breadcrumbs; shape mixture into balls (about 2 tablespoons each) and roll in cracker crumbs. Transfer to a platter and refrigerate for at least 2 and up to 8 hours.

To fry, pour oil to a depth of at least 2 inches in a deep skillet or Dutch oven set over medium-high heat. Heat oil to 360F and, working in batches, fry croquettes, turning occasionally, until well browned on all sides. Transfer browned croquettes to a rack set over a baking rack to cool briefly; serve hot with your favorite dipping sauce.