Myford Chuck question

Hello

This is my first post , so bear with me! I have inherited a super 7 lathe, which is in need of rebuild. Before I start , I’m trying to see what is good and bad . The first test was the Chuck run out , which was around 0.5mm ! The mandrel is near perfectly true, so I stripped the Chuck , cleaned, de rusted etc and reassembled with smear of ACF 50. On reassembly it was still a long way out , the jaws look ok and have been thoroughly cleaned. I found the only way to get the run out to a reasonably acceptable level was to slacken the rear mounting bolts (3 bolts) and gently tap the Chuck in the direction of true and retighten the mounting bolts . The result is a run out of about 0.02mm, which I think is good (I’m not a mechanical engineer btw) . My question is - is this an acceptable practice or indeed normal to do this ? And is it likely to stay true ?
Thanks in advance