@Ronald McD: this is slightly OT, but I was wondering if the use of "they" (and them, their etc) to refer to someone whose gender you don't know was a purely BE thing. I thought so, but I'm not sure. as in, "someone posted a reply to the question but I don't agree with them."
back on topic, you say, "Run for your lives" (Iron Maiden song :D)
and a search in Google yields some examples and confirms my general feeling on this, that in this context 'lives' would be better.
> 650'000 hits for the phrase "..lives"
"I think, technology is very important for our lives, because it gives us many things which help us to improve our lives."
"And if we have no commitment to institutions or movements, the institutions and movements that are important for our lives will decline and fail."
"Once we have embarked on what we feel is important for our lives then our commitment is required."
> 167'000 for "...life"
"Regular checkups are important for our life. If we want to have a long life, we need checkups."
"Water is very important for our life. But these days, the pollution is very serious."
in addition, I also got the feeling that the 'life' version is sometimes used by foreign sites when "lives" would be better. so following this evidence, I'd go with "lives"