Penny:
Ford had big problems with the 1999 Cobras (sub-par intakes, inaccurate HP ratings) and cancelled production for the 2000 model but I don't believe there was a recall for cylinder head problems on the '01's - but I may be mistaken.
In any case, I would try changing the oil - while the engine is hot - at least twice over the next 500 miles. You may just have some unremoved gunk in the engine that is making for a noisy lifter. However, if you started the engine cold after sitting for months - without priming the oil pump - you may well have done some engine damage. Before panicking, I would first do the oil change(s) and give the car a good, long, high-speed run (with fresh oil) to see if the noise subsides - as it well might.
You see, automobile engines are like people in one regard: they need 'exercise'. When they sit, unused, for months, sludge can form in the engine and starting a stone-cold engine with no oil pressure can damage upper cylinder parts or even score the walls. I trust this won't be the case with your Cobra and that a good run will clear out any sludge and restore your 4.6 to it's former quiet glory.
