The following was posted here quite a while back (I saved it):

Personally, I've used nothing but a good synthetic since 1978, and my
wife's 2004 Rodeo only has that problem when it's coming time for an
oil change.  I only change every year or 25,000 miles, due to the
quality of synthetic I use, though filters get changed every 6 months
or 12,500 miles.  I use a 0w30, and once the oil has been changed
(along with the filter, of course), the problem goes away very quickly
(presumably the oil passages get cleaned out, since good quality
synthetics do a nice job of cleaning, also).

You might want to try a good engine cleaning (with a QUALITY, mild
engine cleaner), and try a 0w30 good quality synthetic such as Amsoil
(yes - I'm biased - I've been using it for nearly 30 years and have
results that fully justify my bias//and no, I don't sell it or work
for the company).  Just be cautious with a synthetic if the ½ quart
low oil is due to usage, rather than just a slight under-fill at the
last oil change.  Sometimes if an engine is using oil, it uses it
"even better" upon switching to a synthetic, ironically because of the
excellent cleaning properties of a good synthetic.  Since your wife's
friend's vehicle is a 2000, that might be a factor - check the mileage
first before considering the above idea.  Personally, if it was moving
toward 100,000 miles, I'd be cautious switching over to a synthetic.
But if it's been regularly changed, is tight (i.e. no leaks and no
significant usage between changes), I'd say give it a try before
spending a lot of money on it.  Just don't let it go too long, so it
doesn't cause a more catastophic failure (i.e. big $$$).

Oh - also if the vehicle has been almost exclusively an around-town,
low mileage vehicle, I'd change oil and take it out on an interstate
or major highway for 50-100 miles, then see what's happening with the
noise.  My wife's Rodeo is very sensitive to severe-service (i.e.
around-town driving almost exclusively), and makes all sorts of noises
after a while.  A freeway trip of 100+ miles and it quiets down and
gas mileage leaps up.

Good luck.  Hope this helps and it's not a major engine problem for
your wife's friend.

C.R.

The Rodeo's are known for a tapping noise but not as loud as you
describe.  Often its the injector packs rather than lifters that make
the noise but again, not nearly as loud as you describe.  Most that have
had troubles with lifter noise have cured it by temporarily changing to
a 0w-30w synthetic.

Below is a TSB I found relating to this issue.

Engine Valve Train - Ticking Noise
TICKING SOUND FROM HYDRAULIC VALVETRAIN

SERVICE INFORMATION

Condition:
The above affected vehicles may exhibit a condition of ticking sounds
coming from the valvetrain during normal operation.

Possible Cause:
One or more hydraulic lash adjusters do not fully extend due to varnish
build-up inside. This condition results from exceeding the required oil
and filter change intervals. Severe driving conditions require more
frequent oil and filter changes. (Refer to appropriate Owner's Manual or
Workshop Manual for details.)

Correction:
A typical repair for the condition may involve the replacement of the
affected rocker arm(s), and rocker shaft(s). However, follow the
information in this bulletin to perform an oil/filter change using 0W-30
Mobil 1 synthetic engine oil, prior to replacing any valvetrain component.

NOTE : Although the current recommended engine oil for these engines is
10W-30 API SJ, the 0W-30 synthetic engine oil allows air in the
hydraulic lash adjusters to bleed out quickly and removes the varnish
that is preventing hydraulic lash adjuster piston travel.

Service Procedure
1. Drain the engine oil, replace the oil filter with a Genuine Isuzu oil
filter, and refill the crankcase with 0W-30 Mobil 1 synthetic engine oil.

2. With the engine warm, run it at 2,500 rpm for 30 minutes.

^ If the ticking noise goes away, return the vehicle to the customer.

^ If the ticking noise persists, proceed with step 3.

3. Let the motor run at idle and use a stethoscope or Steel screwdriver
to determine which bank is noisy. Once you have determined the location,
turn the key off. (Figure 1)

4. Remove the cylinder head cover on the noisy bank.

5. Inspect each rocker arm for clearance at the valve (when the rocker
is on the base circle of the cam and the valve is closed). The noisy
rocker arms are the ones with clearance. (Figure 2)

NOTE : Each cylinder head has one oil pressure relief valve that
controls oil pressure to its rocker arms. If all rocker arms on one
cylinder head have clearance and/or the rocker arm pivot shaft is worn,
then the cylinder head oil pressure relief valve may be stuck open. In
this case, refer to the appropriate Workshop Manual for additional
troubleshooting procedures.

6. Remove the ticking rocker arm assembly, and inspect the wear pattern
of the hydraulic lash adjuster surface that contacts the valve stem (the
intake rocker arm is located under the camshafts, which require timing
belt removal).

7. Carefully remove the Hydraulic Lash Adjuster(s) from the Rocker Arms
using your fingers. (Figure 4)

IMPORTANT : Do not damage the O-Ring on the outside of the Hydraulic
Lash Adjuster, or you will have to replace the entire rocker arm (the
Hydraulic Lash Adjuster cannot be ordered separately). When replacing an
exhaust rocker arm, replace its intermediate rocker arm too.

8. Insert a paper clip into the hole at the top of the Hydraulic Lash
Adjuster and depress the spring loaded check ball, while completely
pushing in the piston at the opposite end. Some traces of oil may come
out of the check ball hole. (Figure 5)

9. Carefully remove and retain the Hydraulic Lash Adjuster O-Ring. Spray
the Hydraulic Lash Adjuster piston with carburetor cleaner to remove any
varnish (while holding the piston in). (Figure 6)

10. Submerge the Hydraulic Lash Adjuster in new cleaning solvent; (while
depressing the check ball) pump the piston repeatedly to allow the
cleaning solvent to penetrate through the Hydraulic Lash Adjuster.
(Figure 7)

11. Submerge the Hydraulic Lash Adjuster in clean 0W-30 Mobil 1
synthetic engine oil, (while depressing the check ball) pump the piston
repeatedly to allow 0W-30 Mobil 1 synthetic engine oil to penetrate
through the Hydraulic Lash Adjuster. Then allow the piston to extend
fully, to fill the Hydraulic Lash Adjuster with oil.

12. Reinstall the Hydraulic Lash Adjuster O-Ring.

13. Lube the Rocker Arm bore that houses the Hydraulic Lash Adjuster
with 0W-30 Mobil 1 synthetic engine oil, then push the Hydraulic Lash
Adjuster back into place.

14. Inspect for leaks at the check ball and piston by attempting to
compress the Hydraulic Lash Adjuster without depressing the check ball
(The Hydraulic Lash Adjuster should not leak or compress).

NOTE : Oil filled Hydraulic Lash Adjuster will hold its valve off the
seat for several crank revolutions. This may cause the engine to run
rough for a short period after starting. To prevent this, select one
cylinder and bleed some oil off the Hydraulic Lash Adjuster (depress the
Check Ball and compress the piston 1/4 of the way down). This will allow
the valve to close. Do not remove all of the oil or the valves spring
and cam will collapse the Hydraulic Lash Adjuster permanently.

15. Reassemble the engine using new cylinder head cover gasket (see
Parts Information) and apply some gasket seal at the corners where the
cam tower gasket and cylinder meet. Torque the Cylinder head cover bolts
to 8 Nm (69 lb. in) using hand tools only.

16. Start the engine and listen for noise.

17. Remind the customer, "More frequent oil changes can prevent varnish
accumulation." Also recommend to use minimum oil rating of: API Service
SG, but SJ is preferred