The number of times the oil and filter are changed in the process of cleaning out an engine is not a fixed number. We keep changing it until it stays clean. Two changes is a common average. The change interval also matters; we use an interval of 200 miles.
There are too many variables to establish a set cleaning routine. The amount and type of internal engine deposits vary, some shops will use cleaning agents added to the oil, engine oil varies in the cleaning agents they contain. All of these change the cleaning time. We stop the changes when the oil remains light brown and somewhat transparent. For gasoline engines dark brown or black oil that is blocks light transfer needs to be changed. Diesel engines accumulate carbon in the oil at too fast a rate to use this method.
The only other way to clean the engine is to take it apart and clean it manually. We always suggest that the valve cover be remove and cleaned when engine deposits are suspected. This allows a much better view of the inside of the engine thereby allowing a more accurate plan to be formulated.
And ,as always, a reminder that an engine should not be run at all if the low oil pressure light is on. Damage happens very rapidly when oil pressure is low.