I think this is a great idea, now that you mention it it's kinda a Duh on my part, should of been one of the first things to suggest after understanding the systemkrazymatt wrote:will also probably put 2-3 washers in the aux. relief spring to try to keep it from just dumping back to sump.
Now that you mention this as an obvious potential area of leakage, do this first before adding the Lucas, inspect it well for contamination and seat scoring etc. and go back with added washers noted. With original cooler spring installed, any change is likely to be a combination of higher oil pressure and some cooler flow. Keep adding washers until you don't get any improvement in pressure/cooling flow, this valve is just a safety relief, and should normally not be flowing at all.
Then switch to Lucas mix if needed.
As long as the oil pressure is in range, no need to worry about testing the lower cooler spring.