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It depends on whether you consider the persons as a group or individually. Eg.
The life of the Romans
The Californian surfers' life
However, in your example:
I give advice to some of my friends how to live their life/lives, but no one seems to take my advice
I don't think you can consider some of your friends as an entity, thus the plural 'their lives' seems more appropriate.
singular or plural 
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