살아오다 is 'to have lived up to this point', with -오다 pulling a whole past life forward to the present, and the -게 adverb says how. It is nearly always about character and formation: 어떻게 살아왔는지 'what kind of life someone has led', 그렇게 살아왔기 때문에 'because that's how I've always lived'. Plain 살았다 just reports a past; 살아왔다 says the pattern is still the person.