Peranakan (per-anak-an). Anak means child. Peranakan means her ancestor from china/India/Arab etc married a malay (or javenese, etc) woman. Peranakan chinese have their own unique culture.
In her case she is peranakan chinese. Liem (Lim)is the 16th bigest clanin china. From her family name i guess she is a Hokkien. For more information about chinese please visit www.chineseroots.com and for more information about peranakan please visit http://baba.demo.kmu.edu.tw/http://baba.demo.kmu.edu.tw/
If she was born in Batavia (Jakarta) maybe you can find her data in Kong Koan Friends (www.kongkoan.org)
Origin of Lin*, Lim*, Lam*, Lum* Famous People in History
The 16th most common last name in China. The Chinese word Lin means forest and the name is related to forest. During the Shang Dynasty, Shang Zhou (1,154 – 1,134 B.C.) had three uncles serving as officials in his administration. They were Bi Gan, Qi Zi and Wei Zi. Due to Shang Zhou’s cruelty and corruption, the people suffered dearly. After urging the king to repent and failed, Wei Zi resigned and Qi Zi pretended to have gone insane. Only Bi Gan remained and continued to urge the king to repent. Bi Gan said, "It’s the servant’s responsibility to correct the master; servants who are afraid of being killed and refrain from telling the truth are not righteous." Due to his stubbornness, Zhou Wang decided to kill Bi Gan. Shang Zhou summoned Bi Gan and said, "I heard that a human heart has 7 openings. If you are loyal, let me take a look at your heart." He then ordered his guards to cut open Bi Gan’s chest for his heart. When the news of Bi Gan’s death reached his wife, she knew that it wouldn’t be long before Zhou Wang would order the execution of the entire family. Being pregnant at the time, Bi’s wife decided to escape to Mu Ye (Wei Hui and Qi of HeNan). She hid in a cave inside a forest until the baby boy was born. She named him Jian. Soon Shang Zhou was overthrown and killed by Zhou Wu Wang. Being the descendents of a righteous official, Jian and his mother were respected by Zhou Wu Wang. Because Jiang was born in the forest, Zhou Wu Wang gave him the name of Lin (forest).