You don't have to take classes to study for a doctorate in Germany. You just need to find a tutor to write Doktorarbeit under his guidance. This Arbeit is a doctoral thesis, and you can get a doctorate if you pass it.
The problem is, Lea is considering whether to study for a doctor directly after finishing a master's degree or to study for a doctor on the job after finding a job-studying is writing a thesis! 1
I hope it helps you! ! They are all German speakers! ! 1