An excerpt from my 2000 WJ Factory Service Manual:
HYDRAULIC LASH ADJUSTER NOISE
(1) Engine oil level too high or too low. This may
cause aerated oil to enter the adjusters and cause
them to be spongy.
(2) Insufficient running time after rebuilding cylinder
head. Low speed running up to 1 hour may be
(3) Turn engine off and let set for a few minutes
before restarting. Repeat this several times after
engine has reached normal operating temperature.
(4) Low oil pressure.
(5) The oil restrictor in cylinder head gasket or the
oil passage to the cylinder head is plugged with
(6) Air ingested into oil due to broken or cracked
oil pump pick up.
(7) Worn valve guides.
(8) Rocker arm ears contacting valve spring
(9) Rocker arm loose, adjuster stuck or at maximum
extension and still leaves lash in the system.
(10) Faulty lash adjuster.
a. Check lash adjusters for sponginess while
installed in cylinder head and cam on camshaft at
base circle. Depress part of rocker arm over adjuster.
Normal adjusters should feel very firm. Spongy
adjusters can be bottomed out easily.
b. Remove suspected lash adjusters, and replace.
c. Before installation, make sure adjusters are at
least partially full of oil. This can be verified by little
or no plunger travel when lash adjuster is depressed.
Perhaps that can help you along.
1995 Jeep Grand Cherokee Laredo, 4.0L 2WD, 355,000 miles.