A wonderful LC substitute for cornstarch or cornflour is called "Guar Gum". It will thicken any liquid either cold or hot. But it REALLY thickens, so start with 1/8 teaspoon to a cup of liquid until you see how it goes.

It gives the same 'transparent' quality to the liquid it thickens (like cornstarch/flour). So gravies don't look the same as with wheat flour.

Guar gum is available in health food stores in North America.