Reasons I think it's lifter:

Responds to oil changes and different oil viscosities
Comes and goes while idling, and is generally gone at higher rpm's
Sounds like a lifter
Sounds like it's closer to firewall than front of engine
Tensioner/chain renewed at 160k miles

I'm assuming the shock is at the front of the engine. Would it go away with revs or oil pressure?

Thanks.