2001 jeep ran hot and cot off and was not registering hot and now lifter is tapping

well either your lucky and you have an exhaust leak (very common on the 4.0 jeep engines) or you have a collapsed lifter, bad wristpin,spun bearing...and other assorted bad mojo.. if it is a 4.0 its very common for them to have exhaust leaks due to the long cast iron manifold. its also common for them to have noisey lifters once they get up there in millage. i have a 2000 jeep and the lifters on it have been making noise for about 40 thousand miles and i havnt had any issues with it. just went to a slightly thicker grade of oil. hope this helps

If you have a hydraulic lifter that is sticking, sometimes marvel oil or lucas engine additive will help. If the noise is caused by wear at the rocker pivot or the lifter/camshaft, it will not. No chemical can replace a worn part.

No...race cars sound better than that!!! If you have a lifter that's sticking, try some marvel oil in there. It won't fix it immediately and if anythings just worn out it may never help. Lifters are hydraulic but non-adjustable. How is the oil pressure? If you don't have a gauge, it may help to either install one or at least have a mechanical gauge attached temporarily and monitored to make sure it's correct. (should be about 40 running hot at idle and a bit higher cold.)
Also...sure it's lifter noise? exhaust manifolds like to crack right where the two head pipes join.

Yes, you can have just a lifter replaced, but it could be other parts as well...like a valve, rocker, or cam shaft. The valve cover needs to come off for a better inspection.

you are going to have to drop the engine oil pan and replace the oil pump.

I suggest Blue Devil products for noisy valve lifters. If they are too worn or one of them is broken , no product will work . The lifters and valves have to be overhauled.

If you have a connecting rod problem, likely it is not the rod itself that has failed, rather, the crankshaft bearing on that rod or the wristpin. Usually though when either has failed, the knocking is an all the time thing, varying with engine rpm. A good tech can usually tell the difference between the two just by listening. A beraing failure is generally also accompanied by a drop in engine oil pressure as well. not so for a wristpin. An intermittent noise (tapping) can also indicate a valve lifter problem... though a lifter can also make noise during a low oil pressure situation. Lifter noise is heard from the top of the engine, both other noises are from underneath.
I would first have a different shop give you a second opinion. If it turns out to be a rod bearing, generally this damages the crankshaft and also sends bearing material throughout the entire engine. To properly repair would require complete teardown and rebuild, or replacement of engine. This does not hold true for lifter or wristpin problems, unless severe, though either can be expensive, even if you do the job yourself..
How long is your powertrain warranty?
Definitely get a second opinion before doing anything else!

sounds like the lifters losed prime! here is a little trick that ive learned add a half off quirt off transmission fluid to the oil to prime the lifter

Check Utube for lifter tap, valve tap, and rod bearing noise. If you pull each spark plug one at a time, plugging it back in after each one, the tapping will go away if it's a rod bearing. At any rate, on your next oil change add some valve-medic or similar additive for valve noise. Make sure you follow direction or you will get massive lifter tap if you pour it into a cold engine.

If you have a mechanical sound and water in oil,it will require engine work...Good Luck..