1. Right now, the lump is not serious, and after the chance it turns out to be serious are very small. So, in this context 'being,' could be interpreted as 'turning out to be.' The chance of the lump turning out to be anything serious isn't very high."
2."Being a doctor myself, I shouldn't forget to take my own health as seriously as I should." Means that since I am a doctor I should take my own health seriously.