The radiator must be sized to handle the heat of the engine,heat is created by the fuel burn,the more fuel,the more power and more heat.
99 percent of the time your LS1 will be producing very little power to pull the truck at legal speeds.And like mentioned above,the modern engine deals with heat rejection better than the original engine.The engineers back then sized to cooling system to handle the maybe 80 actual hp ,and being a truck,they most likely figured it would be pulling a load frequently.
I would say a stock type radiator if it can handle being pressurized to modern standards will be ok.More important,again mentioned above,is having enough cooling fan air flow at low speeds.
