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The lash adjuster on these engines is hydraulic and is self adjusting.
The problem with your vehicle is probably the camshaft and tappet. I have seen many 4.0L engines with worn camshaft lobes and concaved tappets. An easy way to check for worn cam lobes is with the valve cover off, run the engine at idle. Place rags around the cylinder head to reduce oil spillage. Hold the end of a screwdriver or equivalent on top of the suspected rocker arm and other known good rocker arms and feel the movement. The rocker with a worn cam lobe will not "kick" as hard as a good cam lobe.
The only repair for this issue is to replace the camshaft and damaged tappets.
Let me know if I can assist you anymore.
Tappets are also called lifters or lash adjusters. The cam shaft lobe pushes on the tappet which pushes the pushrod up, moving the rocker arm which opens the valve. The tappets are constantly fed engine oil to adjust the slack in the valvetrain and also to lubricat the push rod at the rocker arm. The tappets look like big AA batteries and the cylinder head must be removed in order to replace them.
Yes I think there is an option where you can request an expert. I have not checked out the customer end of this site so I am not sure. Another thing you can do is request me in the title of your question, "I would like Sean to answer this if possible". I have seen posts like that before.
Thank you for your interest.