Archon'* definitely right, the lifters are loud. I had no trouble hearing it from inside the house with the doors & windows shut, but only for the first few minutes when the car had sat overnight. It only ever sounded like a single lifter (at a constant steady frequency), and it got progressively worse within about a month'* time. Just based on my experience with my car, I think the LIM gasket failure was the root cause. It seems to me that UIM failure coolant would primarily get ingested and spit back out the exhaust, as opposed to the LIM gasket allowing it into the lifters and down through the block to the oil pan. That'* just my opinion. Since there seemed to be only one lifter making noise, maybe it was the one closest to the failed LIM coolant passage (?). I still don't know if the coolant had thinned the oil enough that it wouldn't stay in the lifters, or if the coolant had caused some contamination and stickiness in the lifter.

Now about your noise - IF its not using coolant or giving any of the other coolant symptoms, could it be piston slap? I've heard this more on 3.1'* than 3.8'* and it was more of a cold idle 'rattle' of several pistons, not just a single-frequency tick.

Hydraulic lifters will shrink if their inlet holes get blocked; causing them to tick between the pushrod and the cam lobe. One pint of gasoline in with the oil is usually the cure; provided that the cam lobe is not worn.

I've never heard of lifters going flat in a 3800, but I guess it'* possible if there'* large particles floating around in the oil.