I am a Lim on my mom's side. Lim is a very "four-counties" regional pronunciation of what is known in Mandarin as Lin, or in Cantonese as Lum or Lam. Four counties is the old name for the places known as Taishan, Kaiping, Xinhui, and Enping, all counties in Guangdong province, China. I have never heard of Eddie Lim nor do I have ties to Florida but I know my own grandfather lived in quite a few places around the country until he settled in San Francisco. Have you got a death certificate for Eddie Lim? It would have his parents' names on it. You could order one from the state in which he died. Also if you can find a headstone for Eddie Lim it might have some good info in Chinese.