I had some issues with lifters both at start and also after normal warm-up when I was running Rotella 15w-40. The problem was not with the oil but my choosing it!! A switch back to 10w-30 immediately corrected the issue.
You didn't mention what WEIGHT oil you were running but 60 psi cold oil pressure, especially with the cooler temperatures raises a red flag. If by chance you're running a heavier oil in hopes of getting a higher zinc/phosphorus concentration, I'd consider some lighter oil and adding a little Lucas ZDDP Break-in suppliment (not their oil treatment) just to be extra safe.
The oil treatment is a viscosity enhancer and you need to go the other way. I'd do this before I started replacing lifters.
Dave