Is I receive an email signed by a Lee Liu, is Lee the family name and Liu the given name?

It is hard to say, because both Liu and Lee can be Chinese family names. In Chinese culture for name writing, Lee should be the family name and Liu the given name. According to the English writing rules, Liu probably is the family name and Lee the given name.
To ensure that, I need his or her Chinese name.

Thanks for your response. I actually met the individual face-to-face today and was able to ask him the same question. In this case, Lee is the given name and Liu is the family name.