I don't really know about the LS1, or oil pressure related things to it...
But usually, if you have good oil pressure when the oil is cold, and as it warms up it drops, then you have a decent sized internal engine problem. Could be leaking past the bearings, could be the oil pump, etc. When this happens, the oil doesn't make it up to the valvetrain, causing the ticking.
You checked the oil level and condition, I assume...
Does the pressue go up with RPM?