<<Disclaimer: Verify this information before applying it to your situation.>>

Having seen a number of advertisements recently for LJS products battered
in corn flour, I contacted them through their website asking whether these
products and/or their fries would be GF.  I specifically mentioned the
risk of cross-contamination in my question.  The answer is the battered
fish and fries are not GF,  but here is the text of the response, which
includes a list of items that do not contain wheat, oats, barley, or rye:

"The ingredient statement of our batter and crispy fries is listed below:

Batter:  Water, corn starch, yellow corn flour, wheat flour (may be
bleached and enriched with niacin, reduced iron, thiamin mononitrate,
riboflavin, folic acid), salt, monosodium glutamate, spices (including
paprika), leavening (sodium bicarbonate, sodium aluminum phosphate,
monocalcium phosphate), garlic powder, natural flavoring, guar gum.

Crispy Fries:  Potatoes, Partially hydrogenated soybean oil, enriched
bleach flour (wheat flour, niacin, iron, thiamin mononitrate,
riboflavin, folic acid), cornstarch, modified food starch, salt, sugar,
dextrin, leavening (disodium dihydrogen pyrophosphate, sodium
bicarbonate), guar gum, dextrose.

The following products do not contain wheat, rye, barley or oats:

Corn
Baked Potato (where offered)
Green Beans (where offered)
Coleslaw
Side and Garden Salads
All Salad Dressings

All items are fried in the same oil:  partially hydrogenated soybean oil

I hope this helps.