Either is possible, and to add to the confusion, "their" could be used for a single person.

Have a read of this for some ideas:

https://www.englishforums.com/English/TheirLifeOrTheirLives/xwkdz/post.htm

My opinion:

Strictly speaking, people have only one life, so one should always say: their life.

However it is my understanding that it si now accepted to say their lives, depending on the context:

1) if we are talking about people sharing their time together, e.g. a married couple, or people living in the same establishment (like orphanage, prison, nursing home) then you will use the singular: their life.

2) if you talk about people form different places and/or living a different life or do not live together, then you can use the plural form: their lives.

3) there is also the situation where one believe that some people can have more than one life (reincarnation): then, of course, their lives would be appropriate. ;)

Either can be correct, depending on the subject in question and the grammar of the sentence.

If the subject is one individual, or the grammar of the sentence is singular, then it's 'life'.

eg<em> Anybody can take control of their life if they try.</em>

as opposed to

<em>More than a hundred people lost their lives in the tragedy.</em>

Thank you for all your advices.