Clone valve lifter hardness is very hit and miss..
Welded lobe cams can eat them, especially with high spring rates.
I have seen stock cams and stock lifters wear each other out in general purpose clones ( soft metal, poor machining and failure to rotate )
Before you worry about your oil worry about the quality of your valve train components.
GM EOS, and any good turbo rated diesel ol would be fine for break in if you feel its important.
Also there are Synthetics and then there are man made petroleum products called synthetics.