Many LS Swaps utilize the stock cooling system from the swapped vehicle. If the vehicle has a 3 or 4 core radiator that’s in relatively good shape, there’s usually no reason not to reuse it after the swap.
The plumbing of the cooling system may become a bit of a challenge. Most older Chevy trucks had the radiator inlet and outlets on opposite sides. However, LS engines have both the inlet and outlet on the same side. Fortunately, the stock upper radiator hose from most LS GM Trucks can be used to route the hose from the engine to the upper radiator connection.
Finding a lower hose that works for your application may also prove to be a challenge, however, the stock lower hose can generally be trimmed and turned to fit most applications. If not, you may need to use a coat hanger to lay out the needed bends, then make a trip to your local auto part store to find a hose that matches your bends, as well as inlet and outlet sizes.
Unlike small or big block engines, LS engines have a steam port that will need to be plumbed into your system. This can be done a number of ways. Some chose to drill and tap the water pump. Other chose to insert a fitting into their upper radiator hose.