It means forest, and is named after someone who was born in the forest. LIM is the HOKKIEN dialectal pronunciation of 林, which in Cantonese pronunciation would be "LAM", where "LUM" is the Cantonese pronunciation of those who don't really know how to romanize the surname in Chinese and only speaks ENGLISH and so based the pronunciation on the way it's similarly pronounced in English. This 林 is pronounced LIN in Mandarin. [noted -ed]
LIM is the HOKKIEN dialectal pronunciation of 林, which in Cantonese pronunciation would be "LAM", where "LUM" is the Cantonese pronunciation of those who don't really know how to romanize the surname in Chinese and only speaks ENGLISH and so based the pronunciation on the way it's similarly pronounced in English. This 林 is pronounced LIN in Mandarin. [noted -ed]