I didn't say lie, I said omit that information. It is not necessary for a doctor to know, since the treatment will be the same. Disclosing that kind of information to the wrong person could get someone arrested, so, as I think I made clear, anyone who took mifepristone can keep that information private if they choose.
The treatment for any complications will the the same regardless of if a miscarriage is natural or induced (i.e., it is not dangerous to omit that info). Here is a source for that, which includes the following advice from a doctor in the USA:
"Dr. Debora Bartz, an ob-gyn at Brigham and Women’s Hospital in Boston, stresses that people don’t need to tell their doctors if they did a medication abortion. “There is no way for a health care professional to be able to distinguish between a natural miscarriage or a medication abortion if the patient herself doesn’t disclose that she took these medications,” Bartz says—a point on which Grossman and Tucker both agree."