A weak lifter will make noise and not lift the valve at the same time. The carbon will be there, hot or cold, and the idle will not change due to carbon, A compression check should show carbon if over 210psi. But these engines seldom get carbon, due to good oil and lack of torque. Drivers rev the crap out of them to drive them.
I have ICV or small intake leak elsewhere. maybe injector.
Compression test, leak down test, injector test. ignition test, plug change.