Well, I did a little search and you don't have to be a nurse but there are credentials required. If you do not have the credentials, then you would not be eligible to even take the exam.
Clinical Competencies for the lactation consultant can be found on the IBLCE web site. They include the following areas : anatomy and physiology, sociology, psychology, counseling, communication skills, child development, nutrition and medical terminology.
When I had my daughter, one of the LCs that helped me was not a nurse but was certified. She told me that and showed me her ID when she first came to help.