Among Taiwanese and Chinese families from abroad, it is sometimes pronounced and spelled as Lim because many Chinese descendants are part of the Southern Min diaspora that speak Min Nan, Hokkien or  Teochew.
In some cases, the name "Lim" is pronounced and spelled this way among Taiwanese and Chinese families living outside of China. This is because many of these individuals come from a Chinese diaspora that speaks Min Nan, Hokkien, or Teochew.