I heard something from my aunt that someone was told that "Lee" was a poor man's version spelling of the surname, whereas "Li" is the richer version. Now, whoever said this is telling people a pile of crock. "Lee" is an Anglicised version, whereas "Li" is the Americanised version. There is also another version, "Lie", as well. I did a quick search and found that there are many other versions.
I had to blog about it, it's really riling how people pass off remarks like that, especially about Chinese surnames, given that they are regarded highly by the Chinese, it's like passing a huge cultural insult.