Both disagreed on what they should do with Horváth the moment they saw that he was better: continue the treatment there in Lemnowice, a field hospital, or relocate him to a Rehabilitation hospital.
Margarete is trying to follow the normal guides and procedures of discharging patients once they get better, also she was aware of Horváth’s desire to go “home”, so she is more focused on the patient’s best interest and based on her experience, she knew that Horváth was ready to move on.
As opposed to Lucius, who is really concentrated on his accomplishment as a doctor which was something he had never experienced before, he feels like Jesus who resurrected Lazarus. Lucius mentions that he feels a pinch of jealousy towards Margarete and an unspoken competition of who could be the one to claim this victory. He felt very proud of himself. So, I don’t think he is really thinking of what was best for the patient.
I would have to say at the moment they were discussing this disagreement, I was backing Lucius because of the extraordinary outcome of his treatment with Horváth, but immediately when Margarete mentioned that the Cossacks were near and the way she alerted him, nothing good was going to come out of their arrival. That made me change my mind as to what should be done with Horváth and agreed that Margarete was being more precautious than Lucius.