Not always. Normally this phrase means that 'living' was the most important thing to the person, as opposed to working.
Life splits into two: living, and working.
Someone who 'made living his career' would concentrate on enjoying life instead of working - normally they'd work just enough to make sufficient money to survive, and go off to play the rest of the time....a really good idea if you can get away with it!
Student or Learner