Well, first of all I'd suggest to use Google Books, because it refers to books published and edited, a much more educated environment than vanilla Google. You'll find that:
"your professional lives"
About 13,500 results
"your professional life"
About 295,000 results
"your personal and professional lives"
About 9,960 results
"your personal and professional life"
About 54,200 results
Thus the singular is clearly preferred. There are several reasons:
normally you address yourself to an individual, not a group
this is especially the case when you want to be convincing: be personal
even when speaking to a group, it is your rhetorical/oratorical choice to talk about "your lives," in order to differentiate more among them, or to use the more generic "your life," where "life" might be considered by some to be uncountable, even though it can potentially represent a multitude of lives.
To the latter, "life" is considered by various dictionaries as both countable and uncountable.
Moreover, except in some faiths, we think of each of us as having a single life, and not several incarnations here on earth:-)