About Janice C. Lim, MD. Janice C. Lim, MD is a family medicine doctor and primary care doctor who practices at South Gwinnett Family Medicine located at 1800 Tree Ln in Ste. 120 in Snellville, GA 30078 (Gwinnett County). Dr. Janice C. Lim has 15+ years of experience in family medicine. Education.