I think the old servant cares about Nakyum but from what I understood from the translation, he knows that Seungho will have no objection if the medicine is for Nakyum -- meaning he is not actually risking his life here.
Also, I think he is talking about a different kind of medicine here that is not about the fever. The servant talks about a 'replenishing energy' medicine, to what the doctor says that Seungho has plenty and then he acts surprised that the servant is asking for Nakyum (meaning it's not for his fever. The medicine if for other purposes). I think we just figured out how Seungho gets his stamina, lol. It's sweet that the servant is thinking that Nakyum will need the same kind of 'energy replenishment' to keep up with Seungho's sexual prowess.
I don't know, I may be wrong though but I think the deal about expensive medicine was to show that the servant knows Seungho is not sparing expenses when it comes to Nakyum so he reassures the doctor.
He is still doing it behind the master's back.. we don't actually know, if SH won't hurt him, if he finds out..
I don't disagree with you, but I read it differently. I interpret it as him lying to the doctor just to convince the doctor to prescribe it.. I too thought that it could be medicine to boost the sexual libido, but I'm not sure, if they had stuff that worked that well at that time.. Maybe the author will give us more insight into this (very important) medicine in a later chapter?
Can we all please just take a moment to appreciate the old man who is risking his life for Nakyum and ordering medicine without the masters permission (▰˘◡˘▰)