Would you treat a patient with Radium 223 for prostate cancer with mainly bone metastasis if he has a history of osteonecrosis of the jaw bone from bisphosphonate/Denosumab?

This is a good question, and one that has very little evidence to answer. Certainly there is some risk of ONJ due to radium 223 from case reports in the literature. There have also been successful palliative treatments with radium in men with bone mCRPC, despite ongoing ONJ due to bisphosphonates:

Use of Radium-223 Dichloride in Patients With Osteonecrosis of the Jaw Induced by Zoledronic Acid: Report of 2 Cases

Such patients with ONJ should be counseled on the potential risks for worsening ONJ balanced against the improved survival and palliation with radium223. There is no right or wrong answer. Avoidance of denosumab and zoledronic acid and good oral care and oral surgery monitoring in a center of excellence is critical.