Lâm was born in 1919. Lâm's father was Trinh and his mother was Xuyên Đào. His paternal grandparents were Vinh and Tĩnh Nguyễn Huy. He had three brothers and a sister, named Bảng, Hòe, Hạnh and Thái. He has a half-brother and a half-sister, named Mai and Tuyết.