Place fish in a bowl and pour in Italian dressing; marinate in the refrigerator, 30 minutes to 1 hour.
Heat oil in a deep-fryer or large saucepan.
Mix flour, cornmeal, paprika, garlic powder, lemon-pepper seasoning, and pepper together in a resealable bag. Pour beaten eggs into a separate resealable bag.
Remove catfish from the marinade and shake off excess. Discard the remaining marinade. Drop catfish into the bag with eggs and shake to coat. Remove a few catfish at a time from eggs using tongs and transfer to flour mixture; shake to coat.
Cook catfish, working in batches, in the hot oil until fish float to the top and are cooked through, 5 to 7 minutes. Remove cooked fish with tongs or a slotted spoon and drain on paper towel. Season fish sticks with salt while still warm.
