The word 'lay' means unqualified: this an 'ordinary' person without formal training or qualifications. For example, a lay preacher or ( or lay minister) is someone who preaches religion but who has not been ordained as a priest (or imam, rabbi etc). I'd understand 'lay doctor' to be someone who does not have formal qualifications as a medical doctor but who still offers treatment. In western societies, such a person would not be allowed to call themselves a 'doctor' - you might refer to them as 'therapist' (quite a vague term) or 'healer'.