I can shut down and re-start and it will disappear most of the time.
YOU are almost certainly a little low on oil. My 2.7 did exactly that when I failed to put in the full 5.5ish quarts. Little tick at (or VERY soon after) start, but shutting it off and restarting had it gone 'til next cold start. Thought I finally ran into the dreaded timing chain guide problem, but nope. Runs like velvet with the full helping of juice.
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Beercheck, are you saying that the oil capacity issue is that small a tolerance?
I am aware that due to differing circumstances at each oil change, the crankcase and filter do not always drain all (most) of the full book capacity of 6 qts. It rarely (like once) took a full 6 when drained, otherwise more like 5.5 qts. I have had a dipstick showing full and the noise will occur. I can be a 1/2 qt low and it will occur. I have a hard time getting my head around your diagnosis. (Weak oil pump???)
Probably the previous owner did not take care of maintenance as he/she shoulda.
BTW, I also worried some about timing chain issues, but am pretty sure this is a lifter or something. I am fearful of the old fix of running a bit of trans fluid in the intake to clean out the lifter or whatever is causing the problem. Worked for me on older American cars.
And does anyone have opinion on the Lucas oil?
Thanks,
Pat
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2001 GV, H25, automatic, BFG AT KO's, K&N air filter, stock otherwise, 153K miles