If you have good oil pressure, then either you have a supply problem to the top end, knackered tappets or duff cam.
Out of these I would say if it has done any miles and the cam looks ok the tappets are shagged, they don't last forever even if they look good as new, you can't see inside them, which is where the adjusty bit is, it's only a tiny spring on that pushes a tiny ball bearing onto a seat to hold the pressure.
tabetha