besides the oil, the lifter bores should be checked and burnished to make sure the lifters rotate correctly, then break-in the cam with additional oil additive with only the outer springs if using a dual spring setup.
After the cam break-in install the inner springs.

If the lifters were bad, then chances are the cam is also shot.
The metal shavings from the wiped out lifters and cam lobes can scratch the cylinder walls, bearings and oil pump.

I let a cam go to long with a bad lobe lifter and had to have the engine hones, new rings, bearings and oil pump.